最終版: 2020/08/22“日本数学会2020 年度秋季総合分科会

英 文

サ

マ

2020 年 9 月

リ集2020 日 本 数 学 会
秋季総合分科会プログラム期

日2020 年 9 月 22 日（ 火 ）〜 9 月 25 日（ 金 ）連 絡 先E-mail kumamoto20sept mathsoc jp
一般社団法人

代 数 学 幾 何 学 函 数 論 函数方程式論

函数解析学 統計数学 応用数学 トポロジー 無限可積分系

9:40〜12:00 10:00〜12:00 9:00〜10:30 9:30〜11:30
15:30〜16:30
14:15〜15:55 14:15〜16:15

10:00〜11:45 9:00〜12:00 9:50〜11:45 10:00〜12:00 9:30〜12:00
14:15〜15:30
14:30〜16:30

22 日
（火）

企画特別講演

23 日（水）

13:00〜14:00

特別講演 特別講演 特別講演 特別講演

特別講演 特別講演 特別講演 特別講演

14:15〜15:15 16:00〜17:00 11:00〜12:00 16:30〜17:30
16:00〜17:00

14:15〜15:15 14:20〜15:20 15:45〜16:45 14:15〜15:15
15:30〜16:30 15:40〜16:40

代 数 学 幾 何 学 函 数 論 函数方程式論

函数解析学 統計数学 応用数学 トポロジー

10:00〜12:00 10:00〜12:00 9:00〜10:20 9:30〜11:30

10:30〜11:45 9:00〜11:15 9:50〜12:00 10:00〜11:40

特別講演

特別講演 特別講演

特別講演

特別講演 特別講演

13:00〜14:00

11:00〜12:00 13:00〜14:00

13:15〜14:15

13:15〜14:15 10:30〜11:30
13:15〜14:15

日 本 数 学 会 賞 授 賞 式
総合講演· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14:30〜15:00)
日 本 数 学 会 賞 秋 季 賞 受 賞 者 · · · · · · · · · · · · · · · · · · · · (15:15〜16:15)
竹 田 雅 好 (関西大システム理工) · · · · · · · · · · · · · · · · · · · · (16:30〜17:30)

数学基礎論
代 数 学 幾 何 学
および歴史

函数方程式論 実函数論 函数解析学 統計数学 応用数学 トポロジー

9:30〜10:35 9:00〜12:00 9:45〜12:00
14:20〜16:10

9:30〜11:30 10:00〜11:55 10:00〜12:00 9:00〜11:50 9:00〜12:00 10:00〜11:55
14:15〜16:15 14:15〜14:45 14:15〜15:10
14:15〜16:30

24 日
（木）

25 日
（金）

日 本 数 学 会

企画特別講演

13:00〜14:00

特別講演 特別講演 特別講演

特別講演 特別講演 特別講演 特別講演 特別講演 特別講演

10:45〜11:45 14:50〜15:50 16:00〜17:00
16:00〜17:00

16:30〜17:30 15:00〜16:00 15:20〜16:20 14:20〜15:20 16:45〜17:45 14:15〜15:15
15:40〜16:40

数学基礎論
代 数 学
および歴史

函数方程式論 実函数論

応用数学

9:30〜10:50 9:50〜12:00
14:15〜16:15

9:30〜11:30 9:45〜12:00
14:15〜16:15 14:15〜15:15

9:00〜11:45
14:15〜15:15

企画特別講演

13:00〜14:00

特別講演

特別講演 特別講演

特別講演

11:00〜12:00

16:30〜17:30 15:30〜16:30

15:30〜16:30

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3

目次
総合講演

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

企画特別講演1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

数学基礎論および歴史 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

9 月 24 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

9 月 25 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

代数学 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99 月 22 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99 月 23 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

9 月 24 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

9 月 25 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

幾何学 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

9 月 22 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

9 月 23 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

9 月 24 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

函数論 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

9 月 22 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

9 月 23 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31函数方程式論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

9 月 22 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

9 月 23 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

9 月 24 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

9 月 25 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

実函数論

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

9 月 24 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

9 月 25 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

函数解析学 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

9 月 22 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

9 月 23 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

9 月 24 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

統計数学

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

9 月 22 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

9 月 23 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

9 月 24 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

応用数学

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

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4

9 月 22 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

9 月 23 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

9 月 24 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

9 月 25 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

トポロジー . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

9 月 22 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

9 月 23 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

9 月 24 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

無限可積分系. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

9 月 22 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

9 月 23 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

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1

総合講演

総 合

講

演

9 月 23 日（水）2020 年度日本数学会賞秋季賞
日本数学会賞秋季賞受賞者· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (15:15〜16:15)

Autumn Prize Winner
竹 田 雅 好 (関西大システム理工)

ディリクレ形式と緊密性を持つ対称マルコフ過程 · · · · · · · · · (16:30〜17:30)

Masayoshi Takeda (Kansai Univ.)

Dirichlet forms and symmetric Markov processes with tightness property

概 要 We introduce a class of symmetric Markov processes. A symmetric Markov process X on a locallycompact separable metric space E is said to be in Class (T) if it is irreducible, resolvent strong Feller,
and possesses a tightness property, i.e., for any ϵ > 0, there exists a compact set K ⊂ E such thatsupx∈E R1 1K c (x) ≤ ϵ. Here 1K c is the indicator function of the complement of K and R1 is the 1-resolventof X.
We show some spectral properties of a symmetric Markov process in Class (T): the compactness of thesemi-group, the bounded continuity of every eigenfunction, the integrability of the principal eigenfunction,
p-independence of growth bounds of the semigroup.
The definition of the tightness property tells us that the two cases occur; X stays on a compact set K
for almost all time or explodes fast. More precisely, if X is conservative, the tightness property implies
a very strong recurrence property (uniform hyper-exponential recurrence): the process X quickly reaches
each compact set from infinity. On the other hand, if X is not conservative, the tightness property implies
that the lifetime of X is exponentially integrable, and so the process quickly reaches infinity. By using
these probabilistic properties, we can prove the uniform large deviations of Donsker-Varadhan type and theexistence and uniqueness of quasi-stationary distributions for each case.
Applying these facts above to time-changed processes, we can give a necessary and suﬃcient condition for
the integrability of Feynman-Kac functionals or the stability of Gaussian bounds in terms of the principal
eigenvalue of the time changed processes.

最終版: 2020/08/22
企画特別講演

企

画

特

別

講

2

演

9 月 22 日（火）増 本

誠 (山 口 大 創 成 )Makoto Masumoto (Yamaguchi Univ.)

リーマン面の接続 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Continuations of Riemann surfaces

概 要 Let R0 be a Riemann surface of finite genus g. A continuation of R0 is, by definition, a pair (R, ι) ofa Riemann surface R and a conformal embedding ι of R0 into R. We are mainly concerned with the casewhere R0 is an open Riemann surfaces of finite genus g.
If g = 0, then the general uniformization theorem assures us that R0 is conformally equivalent to a domain on
the Riemann sphere. In 1928 Bochner generalized it to the case of higher genus in his study on continuationsof Riemann surfaces, showing that R0 can be realized as a subdomain of a closed Riemann surface of thesame genus g. While a closed Riemann surface of genus zero is essentially unique, this is not the case forclosed Riemann surfaces of positive genus. It is then natural to ask into which closed Riemann surfaces ofgenus g the Riemann surface R0 can be conformally embedded.
Heins first tackled the problem for g = 1, and proved in 1953 that the set of closed Riemann surfaces ofgenus one giving a continuation of R0 is relatively compact in the moduli space of genus one. Four years
later Oikawa formulated the problem in the context of Teichmüller theory, and discovered that the set M(R0 )of marked closed Riemann surfaces of genus g into which R0 can be mapped by a conformal embedding
preserving markings is compact and connected in the Teichmüller space Tg of genus g. In 1987 Shiba
improved Oikawa’s result in the case of genus one by deducing that Oikawa’s set is in fact a closed disk in
T1 , which may degenerate to a singleton, with respect to the Teichmüller distance.
Recently, we have been making great progress in the research on M(R0 ) for general g. In this talk we
discuss, among other things, geometric properties of M(R0 ), characterizations of conformal embeddings of R0
giving rise to boundary points of M(R0 ), and uniqueness of conformal embeddings of R0 into closed Riemannsurfaces of the same genus.
富 安 亮 子 (九 大 I M I)

数理結晶学における格子の問題 · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Ryoko Tomiyasu (Kyushu Univ.)

Lattice problems in mathematical crystallography

概 要 The concept of lattices was originally introduced and studied by August Bravais in botany andcrystallography. Starting from the pioneer works of Bravais, I’d explain about several problems in modern
crystallography and examples for actual applications of the theory of arithmetic quadratic forms I haveobtained so far.

9 月 24 日（木）高 田 佳 和 (熊本大⋆)Yoshikazu Takada (Kumamoto Univ.

⋆)

最良母集団の選択 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Selection of the best population

概 要 We consider the problem of selecting the best one of several populations on the basis of observations fromeach population. The problem has generally been formulated adopting an approach known as the indiﬀerencezone formulation. We also discuss the problem of selecting a subset containing the best population. First
we consider normal populations, and discuss two cases. One is that the best population is the one withthe largest mean, and the other is that the best population is the one with the smallest variance. Next we
consider binomial populations, and select the best one with the highest probability of success. Finally, we
consider the problem of selecting the best component of mean vector of a multivariate normal distribution
and of selecting the best category of a multinomial distribution.

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3

企画特別講演

高 山 信 毅 (神 戸 大 理)

多変数超幾何系と統計 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Nobuki Takayama (Kobe Univ.)

Hypergeometric systems of several variables and statistics

概 要 Special functions such as incomplete gamma functions and error functions are used in statistics.

Hypergeometric functions of several variables also appear in several questions in statistics. However, they
had not been utilized for numerical evaluation of statistical quantities because the evaluation is not easy.
Modern theoretical and computational studies of hypergeometric systems of several variables make theevaluation possible.

9 月 25 日（金）
羽 鳥

理 (新

潟

大⋆) ♭ バナッハ環上の等距離写像 · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Osamu Hatori (Niigata Univ.⋆)

Isometries on Banach algebras

概 要 An isometry is a transformation which preserves the distance between elements of a space. In 1932

Banach exhibited that every surjective isometry T on the space of continuous real-valued functions on acompact metric space such that T (0) = 0 must have the form
T (f ) = λf ◦ φ,where λ is a unimodular function and φ is a homeomorphism. He establised a canonical form which fits inan astonishing number of cases. He, in fact, proved that an isometry preserves the algebraic structures of theunderlying Banach algebras. In this talk we consider the problem “When does an isometry between Banach
algebras as Banach spaces preserve the algebraic structures as Banach algebras?”. Providing some historyof the subject, my goal is to produce a useful resource for mathematicians who are interested in the subject.
Due to my capability, probably I have underestimated the enormity of such subject, what I deliver in thistalk is more of a sampler than a full-blown survey.
後 藤 竜 司 (阪Ryushi Goto大理) ♭ 一般化されたケーラー幾何 · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)(Osaka Univ.)

On generalized Kähler geometry

概 要 A generalized Kähler structure on a manifold is a triple (g, I, J) consisting of a Riemannian metricg compatible with two complex structures I, J satisfying the certain conditions, which has an origin in a
non-linear sigma model in Mathematical physics. However, a generalized Kähler structure has a naturaldescription using the language of Hitchin’s generalized complex geometry, which is a commutative pair(J1 , J2 ) of generalized complex structures equipped with a positivity condition. The deformation-stability
theorem of generalized Kähler structures shows that every holomorphic Poisson structure on a compact Kähler
manifold gives rise to nontrivial deformations of generalized Kähler structures. In Kähler geometry, Fujiki–
Donaldson gave a nice description of scalar curvature as the moment map for hamiltonian diﬀeomorphisms.
In generalized Kähler geometry, one does not have the good notions of Levi–Civita connection and curvature,
yet there still exists a precise framework for moment map and scalar curvature is defined as the moment map.
Then a fundamental question is to understand the existence or non-existence of generalized Kähler structureswith constant scalar curvature.
We study automorphisms of generalized complex manifolds and show that the automorphisms is a reductive Liegroup if there exists a generalized Kähler structure with constant scalar curvature. This is a generalization of
Matsushima–Lichnerowicz obstruction theorem. We also discuss deformations of generalized Kähler structurewith constant scalar curvature.

最終版: 2020/08/22
数学基礎論および歴史

数 学

基

礎

論

お

よ

び

歴

4

史

9 月 24 日（木）9:30〜10:35
1 増 田

茂 (流体数理古典理論研)

Shigeru Masuda(Res. Workshop of Classical Fluid Dynamics)

Study of the Eulerian Integrals by Legendre · · · · · · · · · · · · · · · · · · · · · · · 15
Study of the Eulerian Integrals by Legendre

概 要 (This is the same with that of the 2020’s annual session.) Legendre issues Traité des fonctions

elliptiques et des intégrales eulériennes etc.

in 1825. In this books he discusses Eulerian Integral with

two sorts of integrals, in relation to Euler’s integrals, including his elliptic functions. Legendre complains
Euler’s integral, saying “they have never been occupied to make the calculation easy, nor to fix the degreeof precision of which it is susceptible,” (art. 169) and proposes that some functions are explained with thearcs of circle and of the logarithms. (art. 60, etc.)
2 増 田

茂 (流体数理古典理論研)

Shigeru Masuda(Res. Workshop of Classical Fluid Dynamics)

The complete functions by Legendre · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The complete functions by Legendre

概 要 (This is the same with that of the 2020’s annual session.) In 1825, Legendre defines as the mostimportant function among his elliptic functions, the complete function (=c.f.) F 1 , E 1 and Π1 . Afterward
in modern times, these functions are newly expressed with K, E and Π such as in the study of a quantum
mechanics, where it shows as F 1 = K. We call E and Π c.f.s of newly defined versions, then E = E 1 , Π = Π1 .
Legendre uses the c.f. in variously applied arena, such as Geometry, Mechanics, Construction of the Tables,
Eulerian Integrals, etc. We discuss the c.f. as the original by Legendre, his objects, eﬀects, and so on. cf.
Table 1.
3 増 田

茂 (流体数理古典理論研)

Shigeru Masuda(Res. Workshop of Classical Fluid Dynamics)

Supplements of study of the elliptic functions and Eulerian Integrals by
Legendre · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Supplements of study of the elliptic functions and Eulerian Integrals by
Legendre

概 要 Legendre issues Traité des fonctions elliptiques et des intégrales eulériennes etc. in 1825. As the third

volume, in 1828, he adds the primary, secondary and tertiary supplements. in which, he discusses mainly
the theories on the elliptic functions of his and by Germany Jacobi and Norwegian Abel on the elliptic
functions. These two younger mathematicians issue many challenging results in the same time, in respecting
to Legendre’s theory. Fifty-years-elder Legendre entertains misgivings that his troubles having constructed
his theories since 1811, might come to nothing, because of fecundity of this branch. We will report what is
his say at the last time in his life.
4 真 島 秀 行 (お茶の水女大⋆)⋆)Hideyuki Majima (Ochanomizu Univ.

2022 年, 関孝和 314 年祭等に向けて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Towards the year 2022, the 314th memorial year of SEKI Takakazu

概 要 The year 2022 is various memorial years of mathematics, mathematical history and mathematical:

the 314th year after his death of SEKI Takakazu (?–1708), the 400th year after the publication of “Division
Instruction (Wariznsyo)”, the 300th anniversary of “TAKEBE Katahiro’s Tetsujjutsu-Sankei”, and so on.
We describe research problems towards the year.

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5

数学基礎論および歴史

10:45〜11:45

特別講演

高 瀬 正 仁西欧近代の数学におけるさまざまな泉の造型

Masahito Takase

Shaping the fountains in Modern Western Mathematics

概 要 There are several impressive fountains in the history of the mathematics on which Modern Western

Mathematics is founded as follows:
Descartes’s method of normals
Fermat’s method of tangents
Fermat’s number theory
Leibniz’s analysis of the infinity√

Johann Bernoulli’s beautiful formula log√−1−1 = π2
Euler’s observation on dividing 0 by 0
Euer’s discovery of the concept of function
Gauss’ idea of transfering number theory from rational numbers to Gaussian numbers
The concept of an Abelian equation discovered by Abel
Kronecker’s “Jugendtraum”
Kummer’s idea of ideal prime factors
Jacobi’s inverse problem of Abelian integrals invented by Jacobi
Riemann’s idea of Riemann surfaces
Hartogs’ inverse problem invented by K. Oka
I will explain the significances of returning to the fountains and make a critical observation on comtemporary
mathematics.
11:50〜12:00

歴史部門懇談会

14:20〜16:10
5 鈴 木 仁 哉 ( UL Japan )Masaya Suzuki(UL Japan)

Kleene の三値論理とフェイルセーフ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Kleene’s ternary logic and fail safe

概 要 Kleene’s ternary logic system was devised to explain the behavior of recursive partial functions in his

book. This approarch does not seem to the mainstream in the recursion theory, but the system have studied
as a kind of multi-valued logic by mathematical philosophers. On the other hand, in the safety engineering,
the same logical system as Kleene’s ternary logic was devised for a completely diﬀerent motivation. The
motivation is to make electronic circuits fail safe. Fail safe is an important notion in preventing accidents.
In this talk, we will see the relationship between these systems.
6 関

隆 宏 (新潟大経営戦略本部)

Takahiro Seki

(Niigata Univ.)

対偶を持つ対合的部分構造論理に対する Gentzen 流の形式化 · · · · · · · · · 15

A Gentzen-style formulation for involutive substructural logics with contraposition

概 要 (This abstract is identical with the abstract of MSJ Spring Meeting 2020.) Involutivity, called double-

negation axiom in classical logic, is one of the important additional axioms to intuitionistic substructural
logics. In this talk, we consider a Gentzen-style formulation for some involutive non-associative substructural
logics and show the cut elimination theorem. The logics in our formulation include contraposition axiom,
regarded as a restricted associativity.

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数学基礎論および歴史

7 藤 田 憲 悦 (群 馬 大 理 工)
Kenetsu Fujita (Gunma Univ.)

6

George Boolos’ “The Hardest Logic Puzzel Ever” revisited · · · · · · · · · · 15
George Boolos’ “The Hardest Logic Puzzel Ever” revisited

概 要 Following R. Smullyan, G. Boolos posed the puzzle “The Hardest Logic Puzzle Ever” (1996), andprovided an answer in the form of “iﬀ”. After that, Roberts (2001) and Rabern–Rabern (2008) showed a
simple solution to the puzzle by using the embedded question lemma. We introduce a formalization of such
Knights and Knaves puzzles in term of propositional logic, and observe that the two answers by Boolos andRoberts–Rabern are essentially logically equivalent. This elegant method can be applied to an analysis of
the puzzle in the fantasy film Labyrinth (1986) as well.
8 志 村 立 矢 (日 大 理 工)

Tatsuya Shimura (Nihon Univ.)

強い意味の disjunction property の易しい証明 · · · · · · · · · · · · · · · · · · · · · 15

A simple proof of a stronger version of disjunction property

概 要 We give a stronger version of disjunction property or intermediate propositional logics and give

simple proofs for the results of Gabbay–de Jongh, Wroński and Chagrov–Zakharyashev only depends on thecompleteness of the intuitionistic propositional logic.
9 大 川 裕 矢 (千葉大融合理工)
倉 橋 太 志 (神戸大システム情報)(Chiba Univ.)
Yuya Okawa
Taishi Kurahashi (Kobe Univ.)

部分保存的な文に対する Bennet の結果の一般化 · · · · · · · · · · · · · · · · · · · 15

Generalizations of Bennet’s result on partially conservative sentences

概 要 A sentence φ is said to be Γ-conservative over T if for every Γ sentence θ, if T + φ ⊢ θ, then T ⊢ θ.

For Γ = Σn (resp. Πn ), let Γd = Πn (resp. Σn ). In 1979, Guaspari asked that for any reasonable sequence{Ti }i∈ω of theories, whether there is a Γd sentence which is simultaneously independent and Γ-conservative
over each Ti . For two theories, this problem was investigated by Bennet. He completely characterized theexistence of simultaneously independent and Σn -conservative Πn sentences over two theories.
We generalized Bennet’s results to the case of theories more than two.
10 倉 橋 太 志 (神戸大システム情報)
大 川 裕 矢 (千葉大融合理工)

Taishi Kurahashi (Kobe Univ.)(Chiba Univ.)
Yuya Okawa

解釈可能性論理 IL の部分論理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Sublogics of the interpretability logic IL

概 要 We study modal completeness and incompleteness of several sublogics of the interpretability logic

IL. First, we introduce the sublogic IL− which is valid in all IL− -frames. Then, we prove the modal
completeness of twelve logics between IL− and IL with respect to IL− -frames. At last, we prove that eightnatural sublogics of IL are incomplete with respect to IL− -frames.
11 佐 々 木 克 巳 (南 山 大 理 工)

Katsumi Sasaki (Nanzan Univ.)

Sequent systems without derivations with temporal assumptions · · · · · 15
Sequent systems without derivations with temporal assumptions

概 要 In natural deduction system for classical propositional logic, there are some inference rules withtemporal assumptions, e.g., implication introduction rule and disjunction elimination rule. Prawitz calls
such inference rules improper inference rules, and the others proper inference rules. Here, we distinguishbetween improper and proper derivations. Specifically, we prove that any sequent system for classicalpropositional logic with only one inference rule cut does not allow improper derivations in general, while itallows proper ones. For instance, in such systems, the sequent ⇒ p → q can not derive from the sequentp ⇒ q and axioms using cut. In order to prove the impossibility of improper derivations, we modify truth
valuation and prove completeness for sequent systems having only one inference rule cut.

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7

数学基礎論および歴史

9 月 25 日（金）9:30〜10:50
12 町 出 智 也 (国 立 情 報 学 研)
Tomoya Machide(Nat. Inst. of Information)

Boolean 多項式の連立方程式に関する公式と計算量について · · · · · · · · · · 15
On a formula for systems of Boolean polynomial equations and computational complexity

概 要 It is known a method of transforming a system of Boolean polynomial equations to a single Boolean

polynomial equation. In this talk, we prove a formula for systems of Boolean polynomial equations using
this method. It is also known that a SAT problem (satisfiability problem), which is important in logic andcomputer science, can be transformed to a system of Boolean polynomial equations. We also give results ofcomputational complexity using the formula.
13 宮 部 賢 志 (明 大 理 工)
Kenshi Miyabe(Meiji Univ.)

計算可能な推論における収束速度 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The rate of convergence of computable inductions

概 要 In the theory of inductive inference by Solomonoﬀ, we consider the rate of convergence of computableprediction to the conditional model measure. The Kullback–Leibler divergence is used to measure thediﬀerence between the prediction and the model measure. The results show that, dominance is a necessary
and suﬃcient condition to converge for a larger class of measures. The rates of convergence diﬀer in diﬀerent
cases.
14 只 木 孝 太 郎 (中 部 大 工)

Kohtaro Tadaki (Chubu Univ.)

アルゴリズム的ランダムネスによる量子情報理論の精密化 III · · · · · · · · · 15

A refinement of quantum information theory by algorithmic randomnessIII

概 要 The notion of probability plays a crucial role in quantum mechanics. It appears as the Born rule.

In modern mathematics which describes quantum mechanics, however, probability theory means nothingother than measure theory, and therefore any operational characterization of the notion of probability is
still missing in quantum mechanics. In our former works, based on the toolkit of algorithmic randomness,
we presented an operational refinement of the Born rule, called the principle of typicality, for specifying
the property of the results of quantum measurements in an operational way. In this talk, we refine
and reformulate the theory of quantum error-correction based on the principle of typicality, in order todemonstrate how properly our framework works in practical problems in quantum mechanics.
15 薄 葉 季 路 (早 大 理 工)

Toshimichi Usuba (Waseda Univ.)

On Reinhardt cardinals · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On Reinhardt cardinals

概 要 In ZF, we show that if there is a poset which forces the axiom of choice,then there is no Reinhardt

cardinal.
16 D. A. Mejia(静 岡 大 理 )Diego A. Mejı́a (Shizuoka Univ.)

Lebesgue measure zero modulo ideals · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Lebesgue measure zero modulo ideals

概 要 Lebesgue measure zero subsets of the real line can be characterized, in a combinatorial way, throughthe ideal Fin of finite subsets of the natural numbers. But, what happens if we consider this combinatorialstatement through an arbitrary idea on the natural numbers, instead of the ideal Fin? We present a
dichotomy deciding whether this new property characterizes Lebesgue measure zero or not, and show theconnections of this property with Baire category and with the sigma ideal generated by closed measure zerosets. This is a joint work with Viera Sottova.

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数学基礎論および歴史特別講演
鈴 木 信 行 (静 岡 大 理)

中間述語論理における選言特性と存在特性

Nobu-Yuki Suzuki (Shizuoka Univ.)

The disjunction and existence properties in intermediate predicate logics

8

11:00〜12:00

概 要 We discuss relationships between the disjunction property (DP) and existence property (EP) in inter-mediate predicate logics. These properties are regarded as characteristics of constructivity of intuitionistic
logic. Since existence-quantifier could be written as powerful (possibly infinitary) disjunction, we expectedthat there must be some relationship between them. They are, however, indepedent in intermediate predicate logics. This result contrasts with those e.g., in intuitionistic and modal arithmetic, and also gives anegative answer to Ono’s problem P52 posed in 1987. The key is the quantifier-annihilation axiom Z. This
axiom is abnormal in intermediate logics; but it works when we discuss DP and EP in superintuitionistic
predicate logics. We introduce a condition, Z-normality, that excludes the Z and is a natural condition forreasonable logics. Then, we can show that EP implies DP for Z-normal logics. This result suggests a reason
why Ono’s problem P52 has remained open. We also report some recent results related to DP and EP.
12:10〜12:30

数学基礎論および歴史分科会総会

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9

代数学

代

数

学

9 月 22 日（火）9:40〜12:00
1 渡 部 隆 夫 (阪大 中 鈴 絵 (鳴

大

理)

尾

高)

Takao Watanabe (Osaka Univ.)
Suzue Ohnaka(Naruo Senior High School)

Sturm 語の反復指数の空隙 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
A gap of the exponents of repetitions of Sturmian words

概 要 By measuring the smallest second occuring time of every factor of an infinite word x, Bugeaud and

Kim introduced a new quantity rep(x) called the exponent of repetition of x. Among other results, Bugeaud√
and Kim proved that 1 ≤ rep(x) ≤ rmax = 10 − 3/2 and rmax is the isolated maximum value when xvaries over the Sturmian words. We determine the value r1 such that there is no Sturmian word x satisfying
r1 < rep(x) < rmax and r1 is an accumulate point of the set of rep(x) when x runs over the Sturmian words.
2 寺 門 康 裕 (中華民国中央研究院) ♭ ホッジ型の mod p 保型形式と代数的モジュラー形式のヘッケ固有値の系· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Yasuhiro Terakado (Academia Sinica)

Hecke eigensystems of automorphic forms (mod p) of Hodge type andalgebraic modular forms

概 要 We show that the systems of prime-to-p Hecke eigenvalues arising from automorphic forms (mod p)

associated to an algebraic group G/Q of Hodge type are the same as those arising from algebraic modular
forms (mod p) associated to an inner form of G. As an application we give an explicit upper bound forthe number of the systems of Hecke eigenvalues of automorphic forms (mod p) associated to the similitudegroup G of a Hermitian form with a totally indefinite quaternionic multiplication. We also show that thesuperspecial locus of the moduli space of abelian varieties of this type, possibly having bad reduction at p,
is non-empty. This is joint work with Chia-Fu Yu.
3 松 坂 俊 輝 (名 大 高 等 研 )Toshiki Matsusaka (Nagoya Univ.)

アイゼンシュタイン級数の三幅対 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Trinity of the Eisenstein series

概 要 We study the weight 2 parabolic/elliptic/hyperbolic Eisenstein series, which gives a harmonic/polar

harmonic/locally harmonic Maass form, respectively. Furthermore, by means of the hyperbolic Eisensteinseries, we can redefine the hyperbolic Rademacher symbol introduced by Duke–Imamoḡlu–Tóth. The symbol
is expressed explicitly in terms of continued fraction coeﬃcients of the corresponding two real quadratic
irrationals.
4 中 川 彬 雄 (千葉大融合理工)
Akio Nakagawa (Chiba Univ.)

対角超曲面のアルティン L 関数と有限体上の一般超幾何関数 · · · · · · · · · 15

Artin L-functions of diagonal hypersurfaces and generalized hypergeometric functions over finite fields

概 要 In this talk, I would like to talk about that the Artin L-function of a diagonal hypersurface D over afinite field associated to a character of a finite group acting on D can be expressed in terms of hypergeometricfunctions and Jacobi sums over the finite field. As an application, I would also like to talk about the Dwork
hypersurfaces and relations among certain hypergeometric functions over diﬀerent finite fields.

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代数学

5 渋 川 元 樹 (神 戸 大 理)

Genki Shibukawa (Kobe Univ.)

10

Some singular values of the elliptic lambda function and incredible cubic
identities · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Some singular values of the elliptic lambda function and incredible cubic
identities

概 要 We propose three kinds of explicit formulas for the elliptic lambda function by elliptic modular

functions. Further, we derive incredible cubic identities as a corollary of our explicit formulas and evaluate
some singular values of the elliptic lambda function.
6 武 田渉 (名 大 多 元 数 理)

Wataru Takeda (Nagoya Univ.)

Erdős last equation のある種の解の存在性について · · · · · · · · · · · · · · · · · 10
On a kind of solutions to the Erdős last equation

概 要 We focus on the solutions to the Erdős last equation n(x1 + · · · + xn ) = x1 · · · xn . Shiu classified thesolutions into the class Cl (n), where l + 1 is the number of xi > 1 and showed that C3 (n) is non-empty if n
is composite, or if n ̸≡ 1 mod 1260 and n ≥ 6. We generalize Shiu’s results for all l and show that C3 (n) is
non-empty if n ̸≡ 1 mod 180180.
7 橋 本 康 史 (琉 球 大 理)
Yasufumi Hashimoto(Univ. of Ryukyus)

モジュラー群に関するセルバーグゼータ関数の臨界領域での値について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Selberg’s zeta function for the modular group in the critical strip

概 要 In this talk, we study the growth of Selberg’s zeta function for the modular group in the critical strip.

8 齋 藤 三 郎 (再生核研・群馬大⋆) ♭松 浦
勉(群馬大数理データ科学教育研究センター)
奥 村博
Saburou Saitoh(Inst. of Reproducing Kernels/Gunma Univ.⋆)
Tsutomu Matsuura (Gunma Univ.)
Hiroshi Okumura

Values of the Riemann zeta function at positive integers by means of
the division by zero calculus · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Values of the Riemann zeta function at positive integers by means of
the division by zero calculus

概 要 This abstract is an arranged version of the 2020 annual meeting talk. In this talk, we will consider

the values of the Riemann zeta function for any positive integers by means of the division by zero calculus.
In particular, the values for odd positive integers were considered as mysterious ones, however, their values
may be considered as in even integers case. We will give both analytical formulas and numerical results. A
basic reference is given in the abstract, but we will talk more up-to-date information. Our purposes of thistalk are to introduce of the division by zero calculus and to show its power.
9 D. Banerjee ( IIIT-Delhi )藤 澤 雄 介南 出
真 (山 口 大 理)
谷 川 好 男Debika Banerjee (IIIT-Delhi)
Yusuke Fujisawa
Makoto Minamide (Yamaguchi Univ.)
Yoshio Tanigawa

On partial sum of Apostol’s Möbius function · · · · · · · · · · · · · · · · · · · · · · 10

On partial sum of Apostol’s Möbius function

概 要 We shall consider an error term in asymptotic formula for the partial sum of Apostol’s Möbius function.

Without any unproved hypothesis, we shall improve an estimate of the error term which was obtained by
Apostol.

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11

代数学

10 飯 高梶 田茂 (学 習 院 大⋆)
光 (あざみ野第一小)

Shigeru Iitaka (Gakushuin Univ.⋆)
Hikaru Kajita(Azaminodaiichi Elementary School)

準メルセンヌ素数と超完全数 NEO · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Quasi-Mersenne primes and super-perfect numbers NEO

概 要 If q = pe − p + 1 + m is a prime where p is a prime,then q are said to be quasi-Mersenne primes

with base p and traslation parameter m. Given a prime p and an integer m, if positive integers a, A satisfy
A = pσ(a) − p + 2 + m and σ(A) = ap − p + 2 + m, then a is said to be super-perfect number NEO.
14:15〜15:15

特別講演
山 本 修 司 (慶 大 理 工 )Shuji Yamamoto (Keio Univ.)

総実代数体のゼータ値と新谷生成類

Zeta values of totally real number fields and the Shintani generatingclass

概 要 In the study of the special values of Riemann zeta and Dirichlet L-functions at negative integers, it isimportant that these values have a common generating function, which is a simple rational function. For
zeta values of arbitrary totally real number fields, similar generating functions were constructed by Shintani
in 1970’s. His idea of using a nicely chosen set of cones is really ingenious, but requires a non-canonicalchoice in the construction. Recently, to understand his construction in a more canonical way, Bannai,
Hagihara, Yamada and the speaker have introduced the Shintani generating class, which is an equivariant
cohomology class on a disjoint union of algebraic tori associated with the totally real field. This cohomology
class is defined in a natural way, and generates zeta values just as in the case of the rational number field.
In this talk, we will first review the classical result of the rational case and Shintani’s work, then explain
the construction of the Shintani generating class and how it generates zeta values.
15:30〜16:30
11 竹 ヶ 原 裕 元 (室 蘭 工 大 理 工)
小 田 文 仁 (近 畿 大 理 工 )Yugen Takegahara(Muroran Inst. of Tech.)
Fumihito Oda (Kindai Univ.)

束バーンサイド環 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Lattice Burnside rings

概 要 There are few generalizations of Burnside rings of finite groups which are abstract Burnside rings.

Recently, we defined a lattice Burnside ring, which is a generalization of Burnside rings of finite groups
and is an abstract Burnside ring, and obtained various results on the ring structure. The slice Burnsidering defined by S. Bouc is an example of a lattice Burnside ring, but we gave another new example andinvestigated the detailed ring structure.
12 島 倉 裕 樹 (東 北 大 情 報)

Hiroki Shimakura (Tohoku Univ.)

On automorphism groups of the holomorphic VOAs associated with
Niemeier lattices and the −1-isometries · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On automorphism groups of the holomorphic VOAs associated with
Niemeier lattices and the −1-isometries

概 要 Recently, it has been proved that there exist exactly 70 holomoprhic VOAs of central charge 24 whose

weight one Lie algebras are non-trivial. One of the next projects is to determine the automorphism groupsof holomorphic VOAs of central charge 24. We discuss the 14 cases related to Niemeier lattices and the−1-isometries.

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代数学

13 B. Mühlherr ( Univ. Giessen )縫 田 光 司 (東 大 情 報 理 工)

Bernhard Mühlherr (Univ. Giessen)(Univ. of Tokyo)
Koji Nuida

12

Locally finite continuations and Coxeter groups of infinite ranks · · · · · 15
Locally finite continuations and Coxeter groups of infinite ranks

概 要 In some previous works on the isomorphism problem in Coxeter groups, certain special kind of

subgroups called finite continuations have played a central role. However, the definition of finite continuations
assumes finiteness of the rank (cardinality of generating set) of the underlying Coxeter group and is in
general not available in the infinite rank cases. In our present work, we propose a generalization of finite
continuations to the infinite rank cases (which itself is also defined for arbitrary groups), and study how theprevious results in the finite rank cases do or do not extend to the infinite rank cases.

9 月 23 日（水）10:00〜12:00
14 榎 園誠 (東 京 理 大 理 工)
堀 口 達 也 (阪 市 大 数 学 研)
長 岡 高 広 (京 大 数 理 研)
土 谷 昭 善 (東 大 数 理)
Makoto Enokizono(Tokyo Univ. of Sci.)
Tatsuya Horiguchi (Osaka City Univ.)
Takahiro Nagaoka (Kyoto Univ.)
Akiyoshi Tsuchiya (Univ. of Tokyo)

Uniform bases for ideal arrangements · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Uniform bases for ideal arrangements

概 要 In this talk, we explain uniform bases for the ideal arrangements. In particular, explicit uniform bases

are presented on each Lie type. Combining the explicit uniform bases with the work of Abe–Horiguchi–
Masuda–Murai–Sato, we also obtain explicit presentations of the cohomology rings of regular nilpotent
Hessenberg varieties in all lie types.
15 榎 園誠 (東 京 理 大 理 工)
堀 口 達 也 (阪 市 大 数 学 研)
長 岡 高 広 (京 大 数 理 研)
土 谷 昭 善 (東 大 数 理)
Makoto Enokizono(Tokyo Univ. of Sci.)
Tatsuya Horiguchi (Osaka City Univ.)
Takahiro Nagaoka (Kyoto Univ.)
Akiyoshi Tsuchiya (Univ. of Tokyo)

An additive basis for the cohomology rings of regular nilpotent Hessenberg varieties · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

An additive basis for the cohomology rings of regular nilpotent Hessenberg varieties

概 要 In this talk, we explain an additive basis for the cohomology ring of a regular nilpotent Hessenberg

variety which is obtained by extending all cohomology classes of smaller regular nilpotent Hessenberg
varieties. In particular, all of the cohomology classes of smaller regular nilpotent Hessenberg varieties arelinearly independent.

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13

代数学

16 百 合 草 寿 哉 (東 北 大 理)
青 木 利 隆 (名 大 多 元 数 理 )Toshiya Yurikusa (Tohoku Univ.)
Toshitaka Aoki (Nagoya Univ.)

Complete special biserial algebras are g-tame · · · · · · · · · · · · · · · · · · · · · · 15
Complete special biserial algebras are g-tame

概 要 The g-vectors of two-term presilting complexes are important invariant. We study a fan consistingof all g-vectors for a complete gentle algebra. We show that any complete gentle algebra is g-tame, bydefinition, its fan is dense. Our main ingredients are their surface model and their asymptotic behavior
under Dehn twists. On the other hand, it is known that any complete special biserial algebra is a factor
algebra of a complete gentle algebra and the g-tameness is preserved under taking factor algebras. As aconsequence, we get the g-tameness of complete special biserial algebras.
17 淺 井 聡 太 (阪 大 情 報)
Sota Asai(Osaka Univ.)

ねじれ類がなす束における広大区間 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Wide intervals in lattices of torsion classes

概 要 This talk is based on a joint work with Calvin Pfeifer. For a fixed abelian length category A, theposet tors A of torsion classes in A is a lattice. Any interval [U, T ] in tors A is a sublattice of tors A, andthe diﬀerence between the two torsion classes U and T is described by the subcategory W := U ⊥ ∩ T .
Motivated by τ -tilting reduction of Jasso, we mainly studied the case that W is a wide subcategory of A;
such [U, T ] are called wide intervals. In this talk, I will explain our main result that a wide interval [U, T ]is isomorphic to the lattice tors W of torsion classes in the abelian category W. If time permits, I would
like to talk about some characterization of wide intervals obtained in our work.
18 臼 井智 (東 京 理 大 理) ♭ Comparison between the Yoneda product with the cup product on Tate–
Hochschild cohomology for Frobenius algebras · · · · · · · · · · · · · · · · · · · · · 15

Satoshi Usui (Tokyo Univ. of Sci.)

Comparison between the Yoneda product with the cup product on Tate–
Hochschild cohomology for Frobenius algebras

概 要 For a Frobenius algebra, there are two ways of defining its Tate–Hochschild cohomology: the firstway uses the notion of complete resolutions; the second makes use of the one of singularity categories.
In the 1990s, using a certain complete resolution of a given Frobenius algebra, Sanada showed that theTate–Hochschild cohomology algebra based on the complete resolution is a graded commutative algebra.
On the other hand, Wang recently proved that the Tate–Hochschild cohomology algebra based on the
singularity category of the enveloping algebra of a Frobenius algebra is also graded commutative. In thistalk, we will show the existence and the uniqueness of cup product on Tate–Hochschild cohomology forarbitrary complete resolution of a Frobenius algebra and prove that the two Tate–Hochschild cohomology
algebras are isomorphic.
19 村 上 浩 大 (京大理) ♭ PBW parametrizations and generalized preprojective algebras · · · · · · · 15

Kota Murakami (Kyoto Univ.)

PBW parametrizations and generalized preprojective algebras

概 要 Preprojective algebras have developed representation theory of quantum groups for symply-lacedcases in many years. Recently, Geiß–Leclerc–Schröer defined preprojective algebras for any symmetrizable
GCM and its symmetrizer. Certain varieties which consist of specific modules on these algebras describe
crystal structures via their irreducible components and constructible functions. In this talk, we give nicestratifications of these varieties describing Lusztig’s PBW parametrizations of canonical bases for non-simply
laced cases, and then we try to give the polytopal descriptions of these parametrizations in Grothendieckgroups of module categories on generalized preprojective algebras.

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代数学

20 上 田衛 (京Mamoru Ueda

大理)

(Kyoto Univ.)

14

Aﬃne super Yangians and rectangular W -superalgebras · · · · · · · · · · · · · 15
Aﬃne super Yangians and rectangular W -superalgebrasb
概 要 We construct a homomorphism from the aﬃne super Yangian Yε1 ,ε2 (sl(m|n))to the universal enveloping algebra of a rectangular W -superalgebra W k (gl(ml|nl), (l(m|n) )) for all m ≠ n and m, n ≥ 2. We also
show that the image of this homomorphism is dense provided that k + (m − n)(l − 1) ̸= 0.
13:00〜14:00

特別講演
岡 田 聡 一 (名 大 多 元 数 理)

Soichi Okada(Nagoya Univ.)

Schur の Q 関数とその一般化
Schur’s Q-functions and their generalizations

概 要 Schur’s Q-functions are a family of symmetric functions introduced by Schur in 1991 in order todescribe the characters of irreducible projective representations of symmetric groups. They play a similarrole for projective representation to Schur functions (Schur’s S-functions) for linear representations ofsymmetric groups. Later it turns out that Schur’s Q-functions appear in various situations parallel to Schurfunctions.
In this talk, first we review several identities for Schur’s Q-functions and provide new transparent proofs tothem by using general formulas such as Pfaﬃan analogues of the Cauchy–Binet formula and the Ishikawa–
Wakayama minor-summation formula. Next we introduce and study a generalization of Schur’s Q-functions,which includes Ivanov’s factorial Q-functions and the t = −1 specialization of Hall–Littlewood functions
associated with the classical root systems. In the last part, we focus on symplectic Q-functions, which are
obtained by putting t = −1 in the Hall–Littlewood functions associated to the root system of type C. We
establish a tableau description and a Pieri-type rule, and discuss some conjectures including the positivity
conjecture of structure constants.

9 月 24 日（木）9:00〜12:00
21 日 比 孝 之 (阪 大 情 報)
木 村 杏 子 (静 岡 大 理)
松 田 一 徳 (北 見 工 大 工)
A. Van Tuyl (McMaster Univ.)
Takayuki Hibi (Osaka Univ.)
Kyouko Kimura (Shizuoka Univ.)
Kazunori Matsuda(Kitami Inst. of Tech.)
Adam Van Tuyl (McMaster Univ.)

The regularity and h-polynomial of Cameron–Walker graphs · · · · · · · · 15

The regularity and h-polynomial of Cameron–Walker graphs

概 要 Fix an integer n ≥ 1, and consider the set of all connected finite simple graphs on n vertices. For each

G in this set, let I(G) denote the edge ideal of G in the polynomial ring R = K[x1 , . . . , xn ]. We initiate
a study of the set RD(n) ⊆ N2 consisting of all the pairs (r, d) where r = reg(R/I(G)), the Castelnuovo–
Mumford regularity, and d = deg hR/I(G) (t), the degree of the h-polynomial. In particular, we identify sets
A(n) and B(n) such that A(n) ⊆ RD(n) ⊆ B(n). When we restrict to the family of Cameron–Walker
graphs on n vertices, we can completely characterize all the possible (r, d).

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15

代数学

22 土 谷 昭 善 (東 大 数 理)
日 比 孝 之 (阪 大 情 報 )Akiyoshi Tsuchiya (Univ. of Tokyo)
Takayuki Hibi (Osaka Univ.)

イニシャルイデアルとその深度 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Initial ideals and their depth

概 要 In this talk, given an arbitrary integer d > 0, we construct a homogeneous ideal I of the polynomial

ring S = K[x1 , . . . , x3d ] in 3d variables over a field K for which S/I is a Cohen–Macaulay ring of dimension
d with the property that, for each of the integers 0 ≤ r ≤ d, there exists a monomial order <r on S withdepth(S/in<r (I)) = r, where in<r (I) is the initial ideal of I with respect to <r .
23 大 杉 英 史 (関西学院大理工)
土 谷 昭 善 (東 大 数 理 )Hidefumi Ohsugi(Kwansei Gakuin Univ.)
Akiyoshi Tsuchiya (Univ. of Tokyo)

Unimodular 配置に付随する nef 分割 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Nef-partitions arising from unimodular configurations

概 要 Reflexive polytopes have been studied from viewpoints of combinatorics, commutative algebra andalgebraic geometry. A nef-partition of a reflexive polytope P is a decomposition P = P1 + · · · + Pr such thateach Pi is a lattice polytope containing the origin. Batyrev and van Straten gave a combinatorial method
for explicit constructions of mirror pairs of Calabi–Yau complete intersections obtained from nef-partitions.
In this talk, by using the algebraic technique on Gröbner bases, we give a large family of nef-partitions
arising from unimodular configurations.
24 柴 田 孝 祐 (岡 山 大 自 然)
柳 川 浩 二 (関西大システム理工)

Kohsuke Shibata (Okayama Univ.)
Kohji Yanagawa (Kansai Univ.)

Minimal free resolutions of Specht ideals for (n − 2, 2) and (d, d, 1) · · · 10
Minimal free resolutions of Specht ideals for (n − 2, 2) and (d, d, 1)Sp

概 要 For a partition λ of a positive integer n, let Iλbe the ideal of R = K[x1 , . . . , xn ] generated by all

Specht polynomials of shape λ. It is known that if R/IλSp is Cohen–Macaulay then λ is of the form either(n − d, 1, . . . , 1), (n − d, d), or (d, d, 1), and it is also known that the converse is true if char(K) = 0.
In this talk, we construct minimal free resolutions of R/IλSp , when char(K) = 0, and λ = (n − 2, 2) or (d, d, 1)
by using Specht modules and operations on Young diagrams.
25 辻 栄 周 平 (北 教 大 旭 川)
黒 田 匡 迪 (日 本 文 理 大 工 )Shuhei Tsujie (Hokkaido Univ. of Edu.)
Masamichi Kuroda(Nippon Bunri Univ.)

B 型 Weyl 部分配置の補空間の格子点に関する組合せ論的相互律 · · · · · · 10
A combinatorial reciprocity for lattice points of the complement of Weyl
subarrangements of type B

概 要 Each subarrangement of the Weyl arrangement of type A, also known as the braid arrangement, isdescribed by using a simple graph. Stanley showed that a combinatorial reciprocity for chromatic symmetricfunctions of simple graphs with the involution of the ring of symmetric functions. The reciprocity is
considered as an Ehrhart-like reciprocity of lattice points of the complement of the corresponding Weyl
subarrangements of type A. We generalize Stanley’s reciprocity for Weyl subarrangements of type B withsigned graphs.

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代数学

26 堀 内淳 (日 本 工 大)
下 元 数 馬 (日 大 文 理)

Jun Horiuchi (Nippon Inst. of Tech.)
Kazuma Shimomoto (Nihon Univ.)

16

Some remarks on weak normality in the mixed characteristic case · · · · 15
Some remarks on weak normality in the mixed characteristic case

概 要 We give some examples of local rings in relation to weak normality and seminormality in the mixed

characteristic case. It is known that two concepts are diﬀerent in the equal prime characteristic case. We
also establish the local Bertini theorem for weak normality in the mixed characteristic case.
27 松 井 紘 樹 (東 大 数 理)

Hiroki Matsui (Univ. of Tokyo)

三角圏のスペクトラムとその可換環論への応用 · · · · · · · · · · · · · · · · · · · · · 15

Construction of spectra of triangulated categories and their applications
to commutative algebra

概 要 Classification of thick subcategories has been one of the main approaches in the studies of triangulated

categories. It has been studied so far in many areas. In this century, a beautiful theory, called tensortriangular geometry, is initiated by Balmer. He defined a topological space for a given tensor-triangulated
category. Using this topological space, he classified radical thick tensor ideals and this result enables us
to do algebro-geometric studies of tensor-triangulated categories. However the Balmer theory is successful,it does not work for triangulated categories that are not tensor triangulated. Such triangulated categories
include two of the most important triangulated categories in commutative algebra: the bounded derived
category and the singularity category of a commutative noetherian ring. In this talk, I will introduce a way
to construct spectra for (not necessarily tensor) triangulated categories and give applications to commutative
algebra.
28 吉 澤毅 (豊 田 工 高 専)

Takeshi Yoshizawa(Toyota Nat. Coll. of Tech.)

Serre 部分圏を用いたねじれ理論の一般化について · · · · · · · · · · · · · · · · · · 10
On the generalized torsion theory associated with a Serre subcategory

概 要 We consider a generalization of the torsion theory associated with a Serre subcategory over a com-mutative Noetherian ring. Aghapournahr and Melkersson defined the Melkersson condition, which is asuitable condition in local cohomology theory. One of our purposes is to show how naturally the concept ofMelkersson condition appears in the context of torsion theories.
29 松 野 仁 樹 (静岡大創造科学技術)

Masaki Matsuno (Shizuoka Univ.)

点スキームが楕円曲線である 3 次元 2 次 AS 正則代数に対応する twisted
superpotential の分類 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The classification of twisted superpotentials of 3-dimensional quadratic
AS-regular algebras whose point schemes are elliptic curves

概 要 It is known that any 3-dimensional quadratic AS-regular algebra is constructed by a unique twisted

superpotential up to scalar multiple. In this talk, we give a complete list of twisted superpotentials of
3-dimensional quadratic AS-regular algebras whose point schemes are elliptic curves in P2 .
30 Haigang Hu(静岡大創造科学技術)

Classification of noncommutative conics associated to symmetric regularsuperpotentials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Haigang Hu(Shizuoka Univ.)

Classification of noncommutative conics associated to symmetric regularsuperpotentials

概 要 Let S be a 3-dimensional quantum polynomial algebra, and f ∈ S2 a central regular element. The

quotient algebra A = S/(f ) is called a noncommutative conic. For a noncommutative conic A, there isa finite dimensional algebra C(A) which determines the singularity of A. In this paper, we mainly focus
on a noncommutative conic such that its quadratic dual is commutative, which is equivalent to say, S
is determined by a symmetric regular superpotential. We classify these noncommutative conics up toisomorphism of the pairs (S, f ), and calculate the algebras C(A).

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17

代数学

31 埴 原 紀 宏 (名 大 多 元 数 理)

Norihiro Hanihara (Nagoya Univ.)

Quasi-equivalence of DG orbit categories · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Quasi-equivalence of DG orbit categories

概 要 In dealing with some unsatisfactory features of triangulated categories, diﬀerential graded (=DG)

categories plays an essential role, which are therefore said to enhance triangulated categories. Motivated bycluster tilting theory, Keller studied when an orbit category of a triangulated category has a triangulated
structure. His approach was to take an orbit at an enhancement, which is called a DG orbit category. We
will present certain uniqueness of DG orbit categories and give an application to cluster tilting theory.
32 柴 田 義 大 (山 口 大 創 成)
倉 富 要 輔 (山 口 大 理 )Yoshiharu Shibata (Yamaguchi Univ.)
Yosuke Kuratomi (Yamaguchi Univ.)

Image summand coinvariant 加群について · · · · · · · · · · · · · · · · · · · · · · · · · 10
On image summand coinvariant modules

概 要 In this talk, we first introduce the concept of relative im-summand coinvariancy. Let M and N be

modules with the projective covers. M is called N -im-summand coinvariant if, for any homomorphism
φ : P → Q such that Im φ is a direct summand of Q, φ(ker p) ⊆ ker q, where (P, p) and (Q, q) are
the projective covers of M and N , respectively. In addition, we give some fundamental properties of
im-summand coinvariant modules, and we show that M is M -im-summand coinvariant if and only if M is
quasi-projective for any module M over a right perfect ring.
14:15〜14:30

代数学分科会総会

14:30〜14:45

2020 年度 (第 23 回) 日本数学会代数学賞授与式

14:50〜15:50

2020 年度 (第 23 回) 日本数学会代数学賞受賞特別講演
亮 (名 大 多 元 数 理) 可換環の加群圏と導来圏における生成問題

高 橋

Ryo Takahashi (Nagoya Univ.)

Generation in module categories and derived categories of commutativerings

概 要 Let R be a ring, and let M, N be R-modules. It is a natural question to ask whether or how one canbuild M out of N by iteration of fundamental operations such as direct sums, direct summands, extensions
etc. This can be thought of not only in module categories but also in derived categories. I will speak about
it in the case where the base ring is commutative.
16:00〜17:00

2020 年度 (第 23 回) 日本数学会代数学賞受賞特別講演
岡 田 拓 三 (佐 賀 大 理 工) ファノ多様体の双有理的森ファイバー構造の研究と有理性問題への応用

Takuzo Okada(Saga Univ.)

Birational Mori fiber structures of Fano varieties and its application torationality problems

概 要 I will talk about birational geometry of Fano varieties. Fano varieties of Picard number one are socalled Mori fiber spaces which appear as outputs of Minimal Model Program (MMP). Outputs of MMP are
not necessarily unique and in general a Fano variety can be birationally transformed into other Mori fiber
spaces. For a given Fano variety of Picard number 1, we can sometimes determine its birational Mori fiber
structure, that is, the Mori fiber spaces birational to the given Fano variety. I will survey results concerning
this kind of birational studies of Fano varieties and explain a direct connection to rationality problems ofalgebraic varieties.

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代数学

18

9 月 25 日（金）9:50〜12:00
33 鈴 木 香 織 (横 浜 国 大 経 営)

Kaori Suzuki (Yokohama Nat. Univ.)

重み付き射影空間への埋め込みの余次元が 4 の場合の Fano 指数が大きい
3 次元 Fano 多様体について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On codim 4 Fano 3-folds with large Fano index

概 要 I will have a talk about the classification of Q-Fano 3-folds with codim 4 using Type I unprojection

for f > 2.
34 山 本 悠 登 (Yuto Yamamoto

IBS-CGP)(IBS-CGP)

トロピカル Calabi–Yau 超曲面の周期 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Periods of tropical Calabi–Yau hypersurfaces

概 要 With a family of toric Calabi–Yau hypersurfaces over a punctured disk, one can associate a logarithmic

variation of polarized Hodge structure (LVPH) on the standard log point in two diﬀerent ways. One is thenatural extension to the origin of the residual B-model variation of Hodge structure in the sense of Iritani,and the other is constructed using the radiance obstruction of the integral aﬃne sphere with singularities
obtained from the family by tropicalization. In the talk, we show that the resulting LVPHs are isomorphic.
35 須 山 雄 介 (阪大理)

Yusuke Suyama (Osaka Univ.)

Fano generalized Bott manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Fano generalized Bott manifolds

概 要 We give a necessary and suﬃcient condition for a generalized Bott manifold to be Fano or weak Fano.

As a consequence we characterize Fano Bott manifolds.
36 須 山 雄 介 (阪大理)

Yusuke Suyama (Osaka Univ.)

特異点の個数が少ないトーリック log del Pezzo 曲面の分類 · · · · · · · · · · 10Classification of toric log del Pezzo surfaces with few singular points

概 要 We give a classification of toric log del Pezzo surfaces with two or three singular points.

37 小 島 秀 雄 (新 潟 大 理)
Hideo Kojima (Niigata Univ.)

対数的小平次元が 1 以下となる開有理曲面の構造について · · · · · · · · · · · 15

Structure of open rational surfaces of logarithmic Kodaira dimension≤1

概 要 Let V be a smooth projective rational surface defined over an algebraically closed field and let D be aconnected curve on V such that S = V − D contains no (−1)-curves, the logarithmic Kodaira dimension ofS ≤ 1 and ρ(V ) − #D < 0, where #D is the number of the irreducible components of D. In this talk, weshow that S contains a surface isomorphic to Σ − C, where Σ is a Hirzebruch surface and C is a connectedcurve. Moreover we classify the possible configurations for C.
38 南

範 彦 (名工大)Norihiko Minami(Nagoya Inst. of Tech.)

高次単線織性=低次単有理性 よりも強い階層構造を与える十分条件の(weighted) complete intersection の場合への適応 · · · · · · · · · · · · · · · · · · · 15

Suﬃcient criteria for some hierachies stronger than Higher Uniruledness = Lower Unirationality, applied to smooth (weighted) complete
intersections

概 要 The speaker’s suﬃcient criteria for some hierachies, which are stronger thanHigher Uniruledness = Lower Unirationality
is applied to the cases of weighted complete intersections. The resulting suﬃcient conditions are rather
complicated, presumably reflecting the richness of the weighted complete intersections, but are simplified toa very satisfactory single inequality, when restricted to complete intersections.

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19

代数学

39 東 谷 章 弘 (阪 大 情 報)

Akihiro Higashitani (Osaka Univ.)

半順序集合に付随する 2 つの凸多面体と組合せ的変異 · · · · · · · · · · · · · · · 15

Two polytopes arising from posets and combinatorial mutations

概 要 Originally, the notion of combinatorial mutations was introduced in the context of mirror symmetry,

and the framework of combinatorial mutations was extended. In this talk, we introduce the notion of
combinatorial mutation for rational polytopes containing the origin. As an application of combinatorial
mutations, we prove that the chain polytope of a poset Π can be obtained by a sequence of the combinatorial
mutation from the order polytope of Π. Namely, the order polytope and the chain polytope of the same
poset Π are mutation-equivalent.
40 藤 田 直 樹 (東 大 数 理)
東 谷 章 弘 (阪 大 情 報 )Naoki Fujita (Univ. of Tokyo)
Akihiro Higashitani (Osaka Univ.)

旗多様体の Newton–Okounkov 凸体と組合せ的変異 · · · · · · · · · · · · · · · · · 15

Newton–Okounkov bodies of flag varieties and combinatorial mutations

概 要 A Newton–Okounkov body is a convex body constructed from a polarized variety with a higher

rank valuation on the function field, which gives a systematic method of constructing toric degenerations ofpolarized varieties. In this talk, we study some kinds of Newton–Okounkov bodies for flag varieties using theframework of combinatorial mutations. By applying iterated combinatorial mutations, we connect specific
Newton–Okounkov bodies of flag varieties including string polytopes, Nakashima–Zelevinsky polytopes, and
FFLV polytopes.
14:15〜16:15
41 加 藤 芳 文 (名 城 大 理 工)
Yoshifumi Kato (Meijo Univ.)

Curvature matrix of the universal bundle of the Grassmann variety · · · 15
Curvature matrix of the universal bundle of the Grassmann variety

概 要 We introduce a local coordinate system to the Grassmann variety Gr(k, n) and express the curvaturematrix of the universal bundle E simply and independently of the choice of local coordinates. We state therelation between the local coordinate system and the Schubert cells of Gr(k, n). By using the system andthe expression of the cells, we obtain explicit integral formulas corresponding Young diagrams.
42 加 藤 芳 文 (名 城 大 理 工)
Yoshifumi Kato (Meijo Univ.)

An observation on Schubert polynomials · · · · · · · · · · · · · · · · · · · · · · · · · · 15
An observation on Schubert polynomials

概 要 We introduce a local coordinate system to the Flag variety and construct a vector field which isexpressed explicitly with respect to the system. Each Schubert cell becomes a union of some flows of vector
field. We associate a certain diagram to the cell and investigate the relation between the diagrams andSchubert polynomials. We present some conjectures.
43 加 藤 芳 文 (名 城 大 理 工)
Yoshifumi Kato (Meijo Univ.)

Explicit integral formulas related to flag varieties · · · · · · · · · · · · · · · · · · 15
Explicit integral formulas related to flag varieties

概 要 We introduce two types of local coordinate system to the flag variety F l(n) and construct a vector

field. Schubert cell is described as the union of flows. The matrix entries of Schubert cell are arranged ina special shape to which we attach a diagram. On the flag variety F l(n), there exists a flag bundle fromwhich we obtain first Chern classes of line bundles. If we substitute these classes to Schubert polynomials,
then their classes become the Poincaré dual of Schubert varieties. In my talk we make explicit forms which
represent the Chern classes and show that Shubert polynomials become very simple after substitution andthere exist explicit integral formulas.

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代数学

44 川 谷 康 太 郎 (大和大理工・阪府大理)
Kotaro Kawatani(Yamato Univ./Osaka Pref. Univ.)

20

単項イデアル整域の安定性条件 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Stability conditions on a principle ideal domain

概 要 Let R be a principle ideal domain which is not a field and D(R) the bounded derived category offinitely generated R-modules. We show that there is no stability condition (in the sense of Bridgeland) on
D(R). Hence the derived category of aﬃne line A1k over a field k has no stability condition.
45 縫 田 光 司 (東 大 情 報 理 工)
(Univ. of Tokyo)

Koji Nuida

楕円曲線上の群構造に関する線型代数のみで完結する証明 · · · · · · · · · · · 10

An elementary linear-algebraic proof without heavy computation for thegroup law on elliptic curves

概 要 The group structure on the rational points of elliptic curves plays several important roles, in mathemat-

ics and recently also in other areas such as cryptography. However, the famous proofs for the group property(in particular, for its associative law) require somewhat advanced mathematics and therefore are not easily
accessible by non-mathematician. This talk introduces a self-contained proof for this property, assuming
mathematical knowledge only at the level of basic linear algebra and not requiring heavy computation.
46 岩 見 智 宏 (九 工 大 工) ♭ Miyaoka–Yau type inequality driven by certain symmetric 2-forms on
extremal neighborhood regarding to the associated 3rd Chern classses· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Tomohiro Iwami (Kyushu Inst. of Tech.)

Miyaoka–Yau type inequality driven by certain symmetric 2-forms on
extremal neighborhood regarding to the associated 3rd Chern classses

概 要 For a semi-stable 3-dimensional extremal neighborhood (X, C) ⊂ C4 with an irreducible and reduced

extremal curve C, the extendability of ∧2 (gr1C Ω1X ) to gr0C ωX under LG-deformation of C contributes tothe existence of flips for (X, C) [S. Mori, 1988]. Based on this fact, the author reported: (a) an analogueof Miyaoka–Yau type inequality with the associated c3 on (X, C) [I., 2018/03], and (b) Higgs sheaves
associated to (X, C) [I., 2019/09]. Following these results, in this talk, the author will report: for notnecessary irreducible nor reduced C, (i) to introduce laminal ideals of C of codimension type 2, withgenelazing the one in [S. Mori, 1988]; (ii) to give a deformation of endomorphisms of Higgs sheaves
associated to (X, C), as generalizing [Y. Miyaoka, 1987] by (b) and (i), and; (iii) to give an analogue ofMiyoaka–Yau type inequality with c3 associated to extended S 2 (gr1C Ω1X ) by (a) and (ii).
47 遊 佐毅 (兵 庫 県 大 物 質)

Takeshi Usa(Univ. of Hyogo)

A family of canonical curves with genus 5 and the degeneration of syzygies · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A family of canonical curves with genus 5 and the degeneration of syzygies

概 要 As an experiment, we apply our technique via an infinitesimal method to study the degeneration of

syzygies for a flat family of canonical curves with genus 5 over a smooth aﬃne curve B. We show that inthis example, the structure of the module T31,1 detects the transversality of the intersection in the Hilbert
scheme H by the curve B and the analytic local divisor D corresponding to the trigonal curves.

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21

幾何学

幾

何

学

9 月 22 日（火）10:00〜12:00
1 竹 内 有 哉 (阪Yuya Takeuchi

大理)(Osaka Univ.)

強擬凸 CR 多様体の Chern 類に対する制約 · · · · · · · · · · · · · · · · · · · · · · · · 15

A constraint on Chern classes of strictly pseudoconvex CR manifolds

概 要 A CR manifold is a real odd-dimensional analog of a complex manifold. In this talk, we give a

constraint on Chern classes of strictly pseudoconvex CR manifolds, which are convex in a holomorphic
sense. We also see the above result is optimal through some examples.
2 竹 内 有 哉 (阪Yuya Takeuchi

大理)(Osaka Univ.)

擬 Einstein 接触形式の存在に関する安定性 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Stability of the existence of a pseudo-Einstein contact form

概 要 A pseudo-Einstein contact form on a strictly pseudoconvex CR manifold is a contact form satisfying

a weak Einstein condition. Recently, the existence of such a contact form has been of great importancesince it is necessary for defining some global CR invariants. In this talk, we show that the existence of apseudo-Einstein contact form is preserved under deformations as a real hypersurface in a complex manifold.
3 竹 内

司 (東 京 理 大 理 )Tsukasa Takeuchi (Tokyo Univ. of Sci.)

具体的な構成による symplectic-Haantjes 多様体と recursion operator の関係性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Examples of 4 or 6-dimensional symplectic-Haantjes manifolds and about
a relationship with recursion operators

概 要 Certain ways of characterizing integrable systems with (1, 1)-tensor field have been investigated, so far.

For example, the construction of recursion operators by G. Marmo, G. Vilasi and more, has been considered,since 1980’s. On the other hand, according to P. Tempesta and G. Tondo stablished new method of using(1, 1)-tensor field for the integrable system, recently. They introduced a concept of symplectic-Haantjes
manifolds to treat completely integrable Hamiltonian system by means of the Haantjes tensor and Haantjes
operator. We show that a geometrical example of 4 or 6-dimensional symplectic Haantjes manifold andrecursion operators. Through these examples, we consider the relationship between recursion operators andHaantjes operators.
4 松 坂 公 暉 (北大理)

Koki Matsuzaka (Hokkaido Univ.)

Toric construction of moduli space of quasi maps from P1 with twomarked points to P1 × P1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Toric construction of moduli space of quasi maps from P1 with twomarked points to P1 × P1

概 要 In general, a toric variety corresponding to a complete fan can be written by using homogeneous

coordinates. This result is due to Cox. On the other hand, the moduli space of quasi maps from P1 withtwo marked points to a toric variety V of multi degree which is introduced by Jinzenji is important in mirror
symmetry and its compactification is also written by using homogeneous coordinates. In this talk, we givethe toric construction of the moduli space of quasi maps in the case of V = P1 × P1 by using methods ofpsuedo-fans and the Min-Value Condition (MVC).

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幾何学

5 河 井 公 大 朗 (学 習 院 大 理)
山 本
光 (東 京 理 大 理)

Kotaro Kawai (Gakushuin Univ.)
Hikaru Yamamoto (Tokyo Univ. of Sci.)

22

変形エルミート・ヤン・ミルズ接続と変形ドナルドソン・トーマス接続の変形理論 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Deformation theory of deformed Hermitian Yang–Mills connections anddeformed Donaldson–Thomas connections

概 要 A deformed Hermitian Yang–Mills (dHYM) connection is a Hermitian connection on a Hermitian line

bundle over a Kähler manifold, which is believed to correspond to a special Lagrangian submanifold via
mirror symmetry. A deformed Donaldson–Thomas (dDT) connection is its analogue over a G2 -manifold
and is believed to correspond to a coassociative submanifold.
The moduli spaces of special Lagrangian submanifolds and coassociative submanifolds are known to be finite
dimensional smooth manifolds by McLean. It is natural to ask whether these connections inherit the same
properties. We show that each of their deformations is controlled by a subcomplex of an elliptic complex
and the moduli space of dHYM connections is always a finite dimensional smooth manifold.
6 池
祐 一 (富 士 通 研)
浅 野 知 紘 (東 大 数 理)

Yuichi Ike (Fujitsu Laboratories Ltd.)Tomohiro Asano (Univ. of Tokyo)

Microlocal theory of sheaves and displacement energy · · · · · · · · · · · · · · · 15
Microlocal theory of sheaves and displacement energy

概 要 We present a sheaf-theoretic method to estimate the displacement energy of compact subsets of acotangent bundle. In the course of the proof, we introduce an interleaving-like distance on some sheaf
category and prove a stability result with respect to Hamiltonian deformation of sheaves. We also givebounds for the displacement energy and the number of intersection points of certain class of rational
Lagrangian immersions, based on the purely sheaf-theoretic method.
7 川 﨑 盛 通 (京 大 数 理 研)
折 田 龍 馬 (新 潟 大 自 然)

Morimichi Kawasaki (Kyoto Univ.)
Ryuma Orita (Niigata Univ.)

シンプレクティック多様体内の擬重集合 · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Pseudoheavy subsets of symplectic manifolds

概 要 Displaceability, non-displaceability of subsets of symplectic manifolds is an interesting problem in

symplectic geometry from the views of dynamical systems and the mirror symmetry. To approach thisproblem, Entov and Polterovich defined the heaviness and superheaviness of subsets of symplectic manifolds.
To generalize their results and solve their problem, we consider the concept of pseudoheaviness. As its
application, we give new examples of non-disolaceable subsets of the product of spheres.
8 佐 々 木 東 容 (早 大 理 工)

Dounnu Sasaki (Waseda Univ.)

カスプ付き双曲曲面上の測地カレントの稠密性問題 · · · · · · · · · · · · · · · · · 15

Denseness property of geodesic currents on a cusped hyperbolic surface

概 要 The space of geodesic currents on a hyperbolic surface were introduced by Bonahon as a generalizationof measured geodesic laminations and have been successfully studied in the case that the surface is closed
or compact (possibly with boundary). One of useful properties is that the space of geodesic currents on
a closed hyperbolic surface can be considered as the measure-theoretic completion of the set of weighted
closed geodesics on the surface, but such a property is not shown in the case that the surface has cusps
due to infinite geodesics connecting two cusps on the surface. We have proved that the space of geodesic
currents on a cusped hyperbolic surface with finite area also has the same denseness property.

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23

幾何学

16:00〜17:00
山 本

特別講演
光 (東 京 理 大 理 )Hikaru Yamamoto (Tokyo Univ. of Sci.)

特殊ラグランジュ部分多様体と平均曲率流とそのミラー

Special Lagrangian submanifolds, mean curvature flows and their mirrors

概 要 A special Lagrangian submanifold was defined by Harvey and Lawson in 1982 as a volume-minimizing

Lagrangian submanifold in a Calabi–Yau manifold. Since Strominger, Yau and Zaslow in 1996 gave physicalimportance to special Lagrangian submanifolds in the context of mirror symmetry, special Lagrangiansubmanifolds have acquired much attention from both mathematicians and physicists. In 2002, Thomas
and Yau conjectured that if a given Lagrangian submanifold is stable (in the sense of their paper) then themean curvature flow starting from it exists for all time and converges to a special Lagrangian submanifold in
its Hamiltonian deformation class. This is the so-called Thomas–Yau conjecture. In 2015, Joyce updated
Thomas–Yau conjecture to make the statement more careful, and it is still widely open. Actually, thisstory is in A-side of mirror symmetry, and there is a corresponding story in B-side. The special object isa deformed Hermitian–Yang Mills connection and a way to get it is a line bundle mean curvature flow. In
the former part of this talk, I would like to give an overview of recent development related to Thomas–Yauconjecture, and in the latter part, give that of studies in B-side which are rapidly developed in these several
years.

9 月 23 日（水）10:00〜12:00
9 富 久 拓 磨 (早 大 理 工 )本 間 泰 史 (早 大 理 工 )Takuma Tomihisa (Waseda Univ.)
Yasushi Homma (Waseda Univ.)

対称空間上の Rarita–Schwinger 作用素の固有値について · · · · · · · · · · · · 10

Spectra of the Rarita–Schwinger operator on some symmetric spaces

概 要 We give a method to calculate spectra of the square of the Rarita–Schwinger operator on compact

symmetric spaces. According to Weitzenböck formulas, the operator can be written by the Laplace operator,
which is the Casimir operator on compact symmetric spaces. Then we can obtain the spectra by using
the Freudenthal’s formula and branching rules. As examples, we calculate the spectra on the sphere, thecomplex projective space, and the quaternionic projective space.
10 権 藤 曉 則 (広 島 大 理)

Akinori Gondo (Hiroshima Univ.)

非コンパクト型対称空間内の弱鏡映等質超曲面 · · · · · · · · · · · · · · · · · · · · · 15

Weakly reflective homogeneous hypersurfaces in noncompact symmetricspaces概 要 Weakly reflective submanifolds are a class of austere submanifolds with certain global symmetry. In

this talk, we give a classification of weakly reflective homogeneous hypersurfaces in noncompact symmetricspaces of low rank. When we approach the classification problem, a necessary condition for a certain typeof homogeneous hypersurfaces to be weakly reflective is obtained. Using this condition, we obtain infinitely
many examples of austere submanifolds which are not weakly reflective.

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幾何学

11 川 又 将 大 (広 島 大 理)
田 丸 博 士 (阪 市 大 理)

Masahiro Kawamata (Hiroshima Univ.)
Hiroshi Tamaru (Osaka City Univ.)24

ある概アーベルリー群上の左不変リッチソリトン計量 · · · · · · · · · · · · · · · 15

Left-invariant Ricci soliton metrics on some almost abelian Lie groups

概 要 For a given Lie group G, the group R× Aut(G) generated by non-zero scalars and automorphisms ofG acts on the space of all left-invariant Riemannian metrics. The orbit space of this action is called themoduli space of left-invariant Riemannian metrics on G. In this talk, for an almost abelian Lie group G
whose moduli space is one-dimensional, we prove that a left-invariant Riemannian metric on G is a Ricci
soliton if and only if the R× Aut(G)-orbit through this metric is an isolated orbit.
12 澤 井洋 (沼 津 工 高 専)

Hiroshi Sawai(Numazu Nat. Coll. of Tech.)Vaisman 可解多様体の構造定理について · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the structure theorem for Vaisman solvmanifolds

概 要 In locally conformal Kähler geometry (for short LCK), it is said to be Vaisman structure if Lee form isparallel with respect to Levi–Civita connection. In this talk, we consider the structure Theorem for Vaisman
solvmanifolds. Moreover, we prove that a Vaisman solvmanifold has no non-Vaisman LCK structure. As acorollary, non-Vaisman LCK solvmanifold has no Vaisman structures. Thus, it is known that Inoue surfaces
and Oeljeklaus–Toma manifold are non-Vaisman LCK solvmanifolds, they have no Vaisman structures.
13 近 藤 裕 司 (広 島 大 理)
田 丸 博 士 (阪 市 大 理)
Yuji Kondo (Hiroshima Univ.)
Hiroshi Tamaru (Osaka City Univ.)

A classification of left-invariant Lorentzian metrics on some nilpotent
Lie groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A classification of left-invariant Lorentzian metrics on some nilpotent
Lie groups

概 要 In this talk, we introduce that there exist exactly six left-invariant Lorentzian metrics on the direct

product of three dimensional Heisenberg group and Euclidean space of dimension n − 3 with n ≥ 4 up toscaling and automorphisms. Only one of these metrics is flat, and the other five metrics are Ricci soliton but
not Einstein. We also characterize the flat metric as the unique closed orbit in terms of the degeneration oforbits. Note that the equivalence class of each left-invariant metric up to scaling and automorphisms canbe identified with an orbit of a certain group action on some symmetric space.
14 多 田 安 輝 (広島大先進理工)
田 丸 博 士 (阪 市 大 理)
Yasuki Tada (Hiroshima Univ.)
Hiroshi Tamaru (Osaka City Univ.)

On poles of quandles and quotients of Alexander quandles by poles · · · 15
On poles of quandles and quotients of Alexander quandles by poles

概 要 Quandle is an algebra which has background in Knot theory. Quandles can be regarded as a

generalization of symmetric spaces. We study about to redifine various concepts of symmetric spaces onquandle. In this talk, we introduce the concept of “poles” on quandles, by refering to the theory ofsymmetric spaces. Then one can naturally define the quotients of quandles by poles. Alexander quandle isan important class of quandle. We prove that the class of Alexander quandles is closed under the quotientsby poles. We also give a criteria for several Alexander quandles to have non-trivial poles, and determine
what their quotients by poles are.

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25

幾何学

15 川 上裕 (金 沢 大 理 工 )本 田 淳 史 (横 浜 国 大 理 工 )小 磯 深 幸 (九 大 I M I )島高)通
峻 祐 (輪

Yu Kawakami (Kanazawa Univ.)
Atsufumi Honda(Yokohama Nat. Univ.)
Miyuki Koiso (Kyushu Univ.)
Syunsuke Tori (Wajima High School)

Lorentz–Minkowski 空間における Heinz 型の平均曲率の評価について · · 15

Heinz-type mean curvature estimates in Lorentz–Minkowski space

概 要 We provide a unified description of Heinz-type mean curvature estimates under an assumption on thegradient bound for space-like graphs and time-like graphs in the Lorentz–Minkowski space. As a corollary,
we give a unified vanishing theorem of mean curvature for these entire graphs of constant mean curvature.
13:15〜14:15

2020 年度日本数学会幾何学賞受賞特別講演 (トポロジー分科会と合同)
枡 田 幹 也 (阪 市 大 理) ♭ トーリックトポロジーにおけるコホモロジー剛性問題

Mikiya Masuda (Osaka City Univ.)

Cohomological rigidity problem in toric topology

概 要 A toric variety is a normal complex algebraic variety with an algebraic action of a C*-torus having an

open dense orbit. The fundamental theorem in toric geometry says that there is a one-to-one correspondence
between toric varieties and fans. Among toric varieties, compact smooth toric varieties, which we call toric
manifolds, are well understood. For instance, their cohomology rings and Chern classes are explicitly
described in terms of the associated fans. The classification of toric manifolds as varieties reduces to theclassification of the associated fans. However, the classification of toric manifolds as smooth manifolds is
not well understood. Related to this, the author and Dong Youp Suh posed the following problem in 2008.
Cohomological rigidity problem (for toric manifolds). Are toric manifolds diﬀeomorphic (or homeomorphic)
if their cohomology rings with integer coeﬃcients are isomorphic as graded rings?
Many partial aﬃrmative solutions to the problem have been obtained but no counterexamples are known
so far. There are several analogues of the problem and two of them are a symplectic analogue and a real
analogue. The former is related to McDuﬀ’s question on the uniqueness of a toric structure on a monotone
symplectic manifold and the latter is related to flat Riemannian manifolds and hyperbolic 3-manifolds ofLoebell type. In this talk, I will overview some development on these problems.

9 月 24 日（木）9:45〜12:00
16 篠 田 裕 佑 (岡 山 大 自 然)
近 藤
慶 (岡 山 大 自 然 )Yusuke Shinoda (Okayama Univ.)
Kei Kondo (Okayama Univ.)

Huber の有限連結性定理の高次元化について · · · · · · · · · · · · · · · · · · · · · · · 15
On suﬃcient conditions to extend Huber’s finite connectivity theorem
to higher dimensions

概 要 In this talk we give suﬃcient conditions to extend Huber’s finite connectivity theorem to higher

dimensions from the radial curvature geometry point of view.
17 藤 岡 禎 司 (京大理)Tadashi Fujioka (Kyoto Univ.)

Alexandrov 空間の崩壊列に対するファイブレーション定理 · · · · · · · · · · · 15
A fibration theorem for collapsing sequences of Alexandrov spaces

概 要 Let a sequence Mj of Alexandrov spaces collapse to an Alexandrov space X where all spaces of

directions are δ-close to the unit sphere. We prove that Mj admits a structure of locally trivial fibration
over X for suﬃciently large j if it has a uniform lower bound ε ≫ δ on the volume of spaces of directions.

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幾何学

26

18 相 野 眞 行 (理 化 学 研 AIP) ♭ ラプラシアンの固有値と球面の積へのグロモフ・ハウスドルフ収束 · · · · 15
Masayuki Aino

(RIKEN)

Eigenvalue of Laplacian and Gromov–Hausdorﬀ convergence to the product of spheres

概 要 Lichnerowicz–Obata theorem is one of the classical theorem about the first eigenvalue of the Laplacianon Riemannian manifolds. Lichnerowicz gave an estimate of the first eigenvalue of the Laplacian for
the Riemannian manifold with positive Ricci curvature, and Obata showed the equality of the estimatecharacterizes the sphere. Moreover, the almost equality case is well studied, and it is known that the
manifold is close to the sphere in the Gromov–Hausdorﬀ sense under some conditions. In this talk, we givea Gromov–Hausdorﬀ approximation to the product of spheres under some conditions.
19 五
小
近
納

明
工 (名 大 多 元 数 理)
林 俊 公 (摂 南 大 理 工)
藤 剛 史 (鹿 児 島 大 理)
谷
信 (名 大 多 元 数 理)

Takumi Gomyou (Nagoya Univ.)
Toshimasa Kobayashi (Setsunan Univ.)
Takefumi Kondo (Kagoshima Univ.)
Shin Nayatani (Nagoya Univ.)

有限グラフの埋め込み不変量の最小化と第 1 固有値の最大化 · · · · · · · · · · 15

Optimal embedding and maximization of the first eigenvalue of a finitegraph

概 要 We introduce an embedding optimization problem for a finite graph. This problem is related to an

optimization problem concerning the smallest nonzero eigenvalue of the graph Laplacian. Göring–Helmberg–
Wappler introduced a diﬀerent embedding problem as a dual of the eigenvalue optimization problem. We
establish a relation between the optimal values of the two embedding problems. It then follows that the
optimal value of our embedding problem is obtained by the optimal value of the eigenvalue optimization
problem. Further, we show that our embedding problem is a dual to a suitably modified version of theeigenvalue optimization problem. We present examples of graphs for which these optimization problems
can be explicitly solved.
20 山 田 大 貴 (総合地球環境学研)
Taiki Yamada(Res. Inst. for Humanity and Nature)

The lower bound of the eigenvalue of the Laplacian on simplicial complex by the Ricci curvature · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The lower bound of the eigenvalue of the Laplacian on simplicial complex by the Ricci curvature

概 要 The Ricci curvature on graphs plays an important role in discrete diﬀerential geometry when we

research global properties of a graph. We define the Ricci curvature on simplicial complexes modifying thedefinition of the Ricci curvature on graphs. Using the i-Laplacian defined by Horak and Jost, we obtain thefollowing main results. It is an estimate of the eigenvalues of the Laplacian on simplicial complexes by the
Ricci curvature.
21 豊 田哲 (工 学 院 大)Tetsu Toyoda (Kogakuin Univ.)

Reshetnyak の定理の非測地的類似 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A non-geodesic analogue of Reshetnyak’s majorization theorem

概 要 Let κ be a real number. Gromov (2001) introduced the Cycln (κ) conditions for all integers n ≥ 4,each of which is a necessary condition for a metric space to admit an isometric embedding into a CAT(κ)
space. We prove an analogue of Reshetnyak’s majorization theorem for (possibly non-geodesic) metricspaces that satisfy the Cycl4 (κ) condition. It follows from our result that for general metric spaces, theCycl4 (κ) condition implies the Cycln (κ) conditions for all integers n ≥ 5.

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27

幾何学

22 加 藤 本 子 (愛 媛 大 理)
尾 國 新 一 (愛 媛 大 理 )(Ehime Univ.)
Motoko Kato
Shin-ichi Oguni (Ehime Univ.)

ある種の Artin 群の非シリンダー的双曲性について · · · · · · · · · · · · · · · · · 15

On acylindrical hyperbolicity of some Artin groups

概 要 It is conjectured that the central quotient of every irreducible Artin group is either virtually cyclic or

acylindrically hyperbolic. We prove this conjecture for Artin groups that are known to be CAT(0) groups
by a result of Brady and McCammond. In particular, we treat Artin groups associated to triangle-freegraphs and Artin groups of large type associated to cones over square-free bipartite graphs.
23 伊 敷 喜 斗 (筑波大数理物質)

Yoshito Ishiki (Univ. of Tsukuba)

距離関数の補間と距離関数の空間 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

An interpolation of metrics and spaces of metrics

概 要 We provide an interpolation theorem of a family of metrics defined on closed subsets of metrizable

spaces. As an application, we observe that various sets of all metrics with properties appeared in metricgeometry are dense intersections of countable open subsets in spaces of metrics on metrizable spaces. For
instance, our study is applicable to the set of all non-doubling metrics and the set of all non-uniformly
disconnected metrics.
16:00〜17:00
金 沢

特別講演
大
篤 (京

理) ♭ Kähler モジュライ空間と三角圏の安定性条件

Atsushi Kanazawa (Kyoto Univ.)

Kähler moduli spaces and stability spaces of triangulated categories

概 要 The complex moduli space of a Calabi–Yau manifold carries a natural Kähler structure, called theWeil–Petersson geometry, and this has been an important tool in the study of Calabi–Yau manifolds.
Inspired by mirror symmetry, we introduce the mirror Weil–Petersson geometry on the Kähler moduli space.
The main tool is the stability conditions of a triangulated category introduced by T. Bridgeland. As anapplication, we investigate the attractor mechanisms of the Kähler moduli space, the mirror of which on thecomplex moduli space was previously studied by G. Moore.

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函数論

函 数

28

論

9 月 22 日（火）9:00〜10:30
1 齋 藤 三 郎 (再生核研・群馬大⋆)
Saburou Saitoh(Inst. of Reproducing Kernels/Gunma Univ.⋆)

Okumura’s disc series can beyond the crucial point of Däumler–Puha’shorn torus models for the Riemann sphere · · · · · · · · · · · · · · · · · · · · · · · · 15
Okumura’s disc series can beyond the crucial point of Däumler–Puha’shorn torus models for the Riemann sphere

概 要 This abstract is an arranged version of the 2020 annual meeting talk. In this talk, we will note a

simple and pleasant new property that an Okumura’s disc series can beyond the crucial point of Däumler
and Puha’s horn torus models for the Riemann sphere by means of the division by zero calculus. We also
will refer to the up to date information on the division by zero calculus.
Key Words: Infinity, discontinuous, point at infinity, stereographic projection, Riemann sphere, horn torus,Däumler Puha’s horn torus, Okumura’s disc series, conformal mapping, division by zero calculus.
2 藤 野 弘 基 (名 大 多 元 数 理)
赤 嶺 新 太 郎 (日 大 生 物 資 源)
Hiroki Fujino (Nagoya Univ.)
Shintaro Akamine (Nihon Univ.)

単葉調和関数および極小曲面・極大曲面に対する境界値問題の対応 · · · · 15

Correspondence between boundary value problems for harmonic mappings, minimal surfaces, and maximal surfaces

概 要 There exists a natural correspondence between (planar) univalent harmonic mappings, minimal

surfaces in the Euclidean space, and maximal surfaces in the Lorentz–Minkowski spacetime. Under thiscorrespondence, we found that some kinds of important boundary value problems for each of these threeobjects correspond to each other: (a) infinite boundary for minimal surfaces, (b) lightlike line segment
boundary for maximal surfaces, and (c) discontinuous boundary value for harmonic mappings. We also
discuss symmetries appearing on the above kinds of surfaces and their conjugations.
3 中 村

豪 (愛 知 工 大 工) ♭ Automorphism groups of compact non-orientable surfaces of genus 6with extremal metric discs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Gou Nakamura (Aichi Inst. of Tech.)

Automorphism groups of compact non-orientable surfaces of genus 6with extremal metric discs

概 要 In this talk we present the groups of automorphisms of non-orientable extremal surfaces of genus

6. Considering those surfaces with automorphisms of the maximum order 10, we obtain two families of
non-orientable extremal surfaces of even genus g admitting automorphisms of the maximum order 2(g − 1).
4 藤 川 英 華 (東 工 大 理) ♭ リーマン面の本質的測地線スペクトラムの漸近的等角不変性 · · · · · · · · · · 15
Ege Fujikawa(Tokyo Tech)

Asymptotically conformal invariance of the essential length spectrum
on a Riemann surface

概 要 The length spectrum is the set of hyperbolic lengths of closed geodesics on a Riemann surface. In thistalk, we introduce the essential length spectrum on a Riemann surface of topologically infinite type, whichis the set of accumulation points on the length spectrum of the Riemann surface. Then, we prove that thisis invariant under the deformation of asymptotically conformal homeomorphisms of Riemann surfaces.

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29

函数論

5 松 崎 克 彦 (早 大 教 育 )Huaying Wei(Jiangsu Normal Univ.)

Katsuhiko Matsuzaki (Waseda Univ.)
Huaying Wei (Jiangsu Normal Univ.)

Strongly symmetric homeomorphisms on the real line with uniform continuity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Strongly symmetric homeomorphisms on the real line with uniform continuity

概 要 We consider certain properties of strongly symmetric homeomorphisms on the real line, which con-stitute the VMO Teichmüller space on it. Diﬀerently from the case on the unit circle, strongly symmetrichomeomorphisms are not preserved under either the composition or the inversion. They are not known tohave quasiconformal extensions whose complex dilatations induce vanishing Carleson measures, either. In
this presentation, however, we show that if uniform continuity is assumed for appropriate mappings, thenthey are preserved by those operations and they have such quasiconformal extensions. Proofs are performedby using harmonic analysis on BMO functions and the Muckenhoupt weights.
6 渡 邉 天 鵬 (京 大 人 間 環 境 )角大 輝 (京 大 人 間 環 境 )Takayuki Watanabe (Kyoto Univ.)(Kyoto Univ.)
Hiroki Sumi

有理写像からなるマルコフ的ランダム力学系のダイコトミー · · · · · · · · · · 15

The dichotomy of Markov random dynamical systems of rational maps

概 要 We consider random holomorphic dynamical systems on the Riemann sphere whose choices of maps

are related to “Markovian” noise. Our motivation is generalizing the theory of i.i.d. random dynamicalsystems to our setting. We show that a generic such system is either stable on average or chaotic with fullJulia set.
11:00〜12:00
角2019 年度 (第 18 回) 日本数学会解析学賞受賞特別講演

大 輝 (京 大 人 間 環 境 )ランダムな複素力学系における様々なランダム性誘起現象とそのメカニ
ズム(Kyoto Univ.)

Various randomness-induced phenomena in random holomorphic dynamical systems and their mechanisms

Hiroki Sumi

概 要 We consider random holomorphic dynamical systems. We see that there are many new phenomena,

so called randomness-induced phenomena, in random holomorphic dynamical systems which cannot holdin determinstic holomorphic dynamical systems. We also consider the mechanisms of the phenomena andsome applications.
14:15〜15:55
7 綾 野 孝 則 (阪 市 大 数 学 研 )V. M. Buchstaber(Steklov Inst. of Math.)

Takanori Ayano (Osaka City Univ.)
Victor M. Buchstaber(Steklov Inst. of Math.)

種数 2 の σ 関数の級数展開の Hurwitz 整性の精密化 · · · · · · · · · · · · · · · · · 15

A refinement for the Hurwitz integrality of the series expansion of thetwo-dimensional sigma functions

概 要 F. Klein constructed the multi-dimensional sigma functions associated with the hyperelliptic curves

as a generalization of the elliptic sigma functions. The hyperelliptic sigma functions play important rolesin the inversion problem of the hyperelliptic integrals. Y. Onishi proved that the series expansion of thehyperelliptic sigma functions around the origin becomes the Hurwitz series over the ring generated by theparameters of the curves. In this talk, we will give a refinement of this result for the case of genus 2.
Our result is based on the fact that the two-dimensional sigma functions satisfy the heat equations in anonholonomic frame, which is derived by V. M. Buchstaber and D. V. Leykin.

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函数論

8 阿 部
誠 (広島大先進理工)島唯 史 (広島大先進理工)
杉 山
俊(日本電気通信システム)
Makoto Abe (Hiroshima Univ.)
Tadashi Shima (Hiroshima Univ.)
Shun Sugiyama(NEC Comm. Systems, Ltd.)30

Cn 上の不分岐 Riemann 領域に対する中間的擬凸性 · · · · · · · · · · · · · · · · 10Intermediate pseudoconvexity for unramified Riemann domains over Cn

概 要 We characterize the q-pseudoconvexity for unramified Riemann domains over Cn , where 1 ≤ q ≤ n, by

the continuity property which holds for a class of maps whose projections to Cn are families of unidirectionallyparameterized q-dimensional analytic balls written by polynomials of degree at most two.
9 日 下 部 佑 太 (阪大理) ♭ 多項式凸集合の補空間の岡性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Yuta Kusakabe (Osaka Univ.)Oka properties of complements of polynomially convex sets

概 要 A complex manifold is called an Oka manifold if the Oka principle for maps from Stein manifolds holds.

Our main theorem states that the complement of a closed polynomially convex set in Cn (n > 1) satisfying acertain condition is an Oka manifold. This gives a positive answer to the well-known long-standing problem
in Oka theory whether the complement of a compact polynomially convex set in Cn (n > 1) is Oka.
10 岩 井 雅 崇 (阪 市 大 数 学 研)
大
理)
江 尻
祥 (阪
松 村 慎 一 (東 北 大 理)

Masataka Iwai (Osaka City Univ.)(Osaka Univ.)
Sho Ejiri
Shin-ichi Matsumura (Tohoku Univ.)

相対的反標準因子の asymptotic base loci について · · · · · · · · · · · · · · · · · · 15

On asymptotic base loci of relative anti-canonical divisors

概 要 We study the base loci including the stable (augmented, restricted) base loci and upper level sets of

Lelong numbers of the relative anti-canonical divisor −KX/Y of an algebraic fiber space ϕ : X → Y . Our
result says that all the above base loci are located in the horizontal direction unless they are empty.
潟大⋆)
11 田 島 慎 一 (新鍋 島 克 輔 (徳 島 大 理 工)

Shinichi Tajima (Niigata Univ.⋆)
Katsusuke Nabeshima(Tokushima Univ.)

D. Barlet の regular meromorphic diﬀerential forms と K. Saito の logarithmic residues · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Computing regular meromorphic diﬀerential forms via Saito’s logarithmic residues

概 要 We consider logarithmic diﬀerential forms along a hypersurface with an isolated singularity in thecontext of computational complex analysis. In our previous work, we study torsion modules and give aneﬀective method for computing them. In this work, we first consider a method for computing regularmeromorphic diﬀerential forms. We show that representatives of regular meromorphic diﬀerential forms canbe computed by using our previous algorithm on torsion modules. Main ideas of our approach are the useof the concept of logarithmic residue and that of logarithmic vector field. Next, we show a link between
logarithmic diﬀerential forms and Gauss–Manin connections, which reveals the role of the torsion module inthe computation of a saturation of Brieskorn lattice of Gauss–Manin connection.

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31

函数論

潟
大⋆)
12 田 島 慎 一 (新鍋 島 克 輔 (徳 島 大 理 工 )Shinichi Tajima (Niigata Univ.⋆)
Katsusuke Nabeshima(Tokushima Univ.)

Versal unfoldings of singular holomorphic foliations —諏訪アルゴリズ
ムの実装— · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
An implementation of the Suwa method for computing versal unfoldingsof codimension one complex analytic singular foliations

概 要 The Suwa method for computing versal unfoldings of holomorphic singular foliations is studied fromthe point of view of computational complex analysis. Based on the theory of Grothendieck local duality on
residues, an eﬀective algorithm of computing versal unfoldings of codimension one complex analytic singularfoliations is obtained.
13 岩 崎 克 則 (北高 田 佑 太 (北

大

理)

大

理)

Katsunori Iwasaki (Hokkaido Univ.)
Yuta Takada (Hokkaido Univ.)

超幾何群から K3 曲面上の Siegel 円板へ · · · · · · · · · · · · · · · · · · · · · · · · · · 15

From hypergeometric groups to Siegel disks on K3 surfaces

概 要 C. T. McMullen constructed K3 surface automorphisms with Siegel disks. The topological entropiesof them must be positive and the underlying K3 surfaces must be transcendental. In this talk we propose acompletely diﬀerent method to construct such automorphisms by using hypergeometric groups and associatedlattices. Here hypergeometric groups, due to F. Beukers and G. J. Heckman, are matrix groups modeledon the monodromy groups of higher-order hypergeometric diﬀerential equations.
16:00〜17:00

特別講演
小 森 洋 平 (早 大 教 育 )双曲コクセター群の増大度について

Yohei Komori (Waseda Univ.)

On the growth rate of hyperbolic Coxeter groups

概 要 In this talk I will give an overview of recent progress on arithmetic aspects of growth related to

hyperbolic Coxeter groups.

9 月 23 日（水）9:00〜10:20
14 本 田 竜 広 (専 修 大 商)
濱 田 英 隆 (九 州 産 大 理 工 )溝 田 裕 介 (九 州 産 大 理 工 )Tatsuhiro Honda (Senshu Univ.)
Hidetaka Hamada(Kyushu Sangyo Univ.)
Yusuke Mizota (Kyushu Sangyo Univ.)

Bohr’s phenomenon on a complex Banach space · · · · · · · · · · · · · · · · · · · 15

Bohr’s phenomenon on a complex Banach space

概 要 In this talk, we discuss about generalisations of the Bohr radius for analytic functions or harmonic

functions on the unit disc in C to that for holomorphic mappings or pluriharmonic mappings on the unit
ball of a complex Banach space.

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函数論(Univ. of Toronto)
15 I. Graham
濱 田 英 隆 (九 州 産 大 理 工)
(Babeş-Bolyai Univ.)
G. Kohr
Ian Graham (Univ. of Toronto)
Hidetaka Hamada(Kyushu Sangyo Univ.)
Gabriela Kohr (Babeş-Bolyai Univ.)

32

Loewner chains and nonlinear resolvents of the Carathéodory family on
the unit ball in Cn · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Loewner chains and nonlinear resolvents of the Carathéodory family on
the unit ball in Cn

概 要 In this talk, we study various properties of nonlinear resolvents of holomorphic mappings in the

Carathéodory family M(Bn ), where Bn is the Euclidean unit ball in Cn .
(Univ. of Toronto)
16 I. Graham
濱 田 英 隆 (九 州 産 大 理 工)
(Babeş-Bolyai Univ.)
G. Kohr(Babeş-Bolyai Univ.)
M. Kohr
Ian Graham (Univ. of Toronto)
Hidetaka Hamada(Kyushu Sangyo Univ.)
Gabriela Kohr (Babeş-Bolyai Univ.)
Mirela Kohr (Babeş-Bolyai Univ.)

g-Loewner chains, Bloch functions and extension operators in complex
Banach spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

g-Loewner chains, Bloch functions and extension operators in complex
Banach spaces

概 要 In this talk, we will show that Φα,β and ΦPk preserves the first elements of g-Loewner chains andnormalized Bloch mappings, where Φα,β : S → S(Ωr ) is the Roper–Suﬀridge type extension operator andΦPk is the Muir type extension operator.
17 濱 田 英 隆 (九 州 産 大 理 工)
(Babeş-Bolyai Univ.)
G. Kohr
Hidetaka Hamada(Kyushu Sangyo Univ.)
Gabriela Kohr (Babeş-Bolyai Univ.)

Support points for families of univalent mappings on bounded symmetric domains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Support points for families of univalent mappings on bounded symmetric domains

概 要 In this talk, we study some extremal problems for the family Sg0 (BX ) of normalized univalent mappings

with g-parametric representation on the unit ball BX of an n-dimensional JB∗ -triple X with r ≥ 2, wherer is the rank of X and g is a convex (univalent) function on the unit disc U, which satisfies some natural
assumptions. We obtain sharp coeﬃcient bounds for the family Sg0 (BX ), and examples of bounded support
points for various subsets of Sg0 (BX ). Our results are generalizations to bounded symmetric domains ofknown recent results related to support points for families of univalent mappings on the Euclidean unit ball
Bn and the unit polydisc Un in Cn .
18 濱 田 英 隆 (九 州 産 大 理 工)
Hidetaka Hamada(Kyushu Sangyo Univ.)

Closed range composition operators on the Bloch space of bounded symmetric domains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Closed range composition operators on the Bloch space of bounded symmetric domains

概 要 Let BX and BY be bounded symmetric domains realized as the unit balls of JB∗ -triples X and Y ,respectively. In this talk, we generalize the Landau theorem to holomorphic mappings on BX by using
the Schwarz–Pick lemma for holomorphic mappings on BX . Next, we give several necessary conditions
or suﬃcient conditions for the composition operators Cφ between the Bloch spaces on BX and BY to bebounded below.

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33

函数論

19 濱 田 英 隆 (九 州 産 大 理 工)
(Babeş-Bolyai Univ.)
M. Iancu(Babeş-Bolyai Univ.)
G. Kohr
Hidetaka Hamada(Kyushu Sangyo Univ.)
Mihai Iancu (Babeş-Bolyai Univ.)
Gabriela Kohr (Babeş-Bolyai Univ.)

Spiralshapelike mappings in several complex variables · · · · · · · · · · · · · · 10

Spiralshapelike mappings in several complex variables

概 要 Let n ≥ 2 and let A ∈ L(Cn ) be such that m(A) > 0. In this talk, we show that if F : Bn → Cn

is a normalized biholomorphic mapping such that F (Bn ) is a bounded strictly pseudoconvex domain withC m boundary with m > 2, then F (Bn ) is polynomially convex if and only if there exists a normalized
automorphism Φ : Cn → Cn such that Φ(F (Bn )) is an A-spirallike domain. This result extends a recent
result due to Arosio, Bracci and Wold in the case of convexshapelike domains.
11:00〜12:00

特別講演
松 村 慎 一 (東 北 大 理) ♭ “非負曲率”を持つ射影多様体に対する構造定理について

Shin-ichi Matsumura (Tohoku Univ.)

Structure theorems on projective manifolds with non-negative curvature

概 要 The study of certain positively curved varieties, which are often formulated with positivity of bisectional

curvatures, tangent bundles, or anti-canonical divisors, occupies an important place in the theory ofclassification of varieties. One of the central problems in this study is to determine the structure of semipositively curved varieties in terms of naturally associated fibrations such as Albanese maps, Iitaka fibrations,or maximally rationally connected fibrations. In this talk, I would like to discuss structure theorems for
projective varieties (more generally compact Kähler manifolds) satisfying various positivity conditions.
More specifically, I will explain structure theorems of maximally rationally connected fibrations for varieties
satisfying the following conditions: (1) Projective manifolds with tangent bundle admitting positively curved
singular hermitian metric. (2) Projective manifolds with semi-positive holomorphic sectional curvature. (3)Projective KLT pairs with nef anti-canonical bundle. The proof is based on singular hermitian metrics onvector bundles, analytic positivity ofdirect image sheaves, the theory of foliations, and so on. A part of thistalk is joint work with F. Campana (Lorraine), J. Cao (Jussieu), M. Iwai (Tokyo), G. Hosono (Tohoku).

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函数方程式論

函

数

方

程

式

34

論

9 月 22 日（火）9:30〜11:30
1 井 上 公 人 (九 大 I M I)
Hiroto Inoue(Kyushu Univ.)

BD I 型の対称領域に付随する行列値 Bratu 方程式 · · · · · · · · · · · · · · · · · · 15
Matrix-valued Bratu equation associated with the symmetric domain oftype BD I

概 要 The Bratu equation is an integrable ordinary equation, that appears as a special case of the Toda

lattice and the Painlevé III equation. In this talk, we introduce a matrix-valued extension of the Bratu
equation. This extension is based on the geometric structure of a symmetric domain G/K. As a main
result, we give its exact solution using the defining function of the symmetric domain. In the talk, wemostly consider the case of the symmetric domain of type BD I.
2 鈴 木 正 俊 (東 工 大 理)

Masatoshi Suzuki (Tokyo Tech)

ある偏微分方程式系と Hermite–Biehler class の整関数. II · · · · · · · · · · · 10

On a system of partial diﬀerential equations and entire functions ofHermite–Biehler class. II

概 要 In the last time, we present an initial value problem for a system of first-order partial diﬀerential

equations in two variables and explain the relationship with entire functions of Hermite–Biehler class. In
this time, we will describe additional issues together with some simple examples.
3 石 田 敦 英 (東 京 理 大 工)Atsuhide Ishida (Tokyo Univ. of Sci.)

分数冪相対論量子系における低速伝播評価について · · · · · · · · · · · · · · · · · 10

On minimal velocity estimate in fractional relativistic mechanics

概 要 In scattering theory, the propagation estimate for the low velocity state plays a conclusive role to prove

the asymptotic completeness of the wave operators. In this study, we prove the minimal velocity estimate
for the massive relativistic Schrödinger operator with fractional powers. In particular, we allow to assume
that the potential functions belong to the broad classes which include the long-range and Coulomb-typesingularities. By virtue of this estimate, the asymptotic completeness for the short-range case can be proved
immediately. This estimate can also be expected to work for further applications (long-range and N -body).
4 宇 佐 美 広 介 (岐 阜 大 工)
ル イ ソ ケ ア (岐 阜 大 工)
Hiroyuki Usami
Luey Sokea(Gifu Univ.)(Gifu Univ.)

Asymptotic forms of solutions of perturbed half-linear equations · · · · · 15
Asymptotic forms of solutions of perturbed half-linear equations

概 要 We consider asymptotic forms of every nontrivial solutions of a class of half-linear ordinary diﬀerential

equations. When these equations reduce to linear equations, it is well known that every nontrivial solutionof them behaves like exponential functions. We will show that this property is still valid even for generalhalf-linear equations under a smallness condition on the perturbation.

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函数方程式論5 柴 田 徹 太 郎 (広 島 大 工 )Tetsutaro Shibata (Hiroshima Univ.)

Asymptotic expansion of oscillatory bifurcation curves of ODEs withnonlinear diﬀusion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Asymptotic expansion of oscillatory bifurcation curves of ODEs withnonlinear diﬀusion

概 要 We consider the global behavior of bifurcation diagrams of nonlinear ODEs with nonlinear diﬀusion,in which some oscillatory nonlinearities are included. In our situation, the bifurcation parameter λ is acontinuous function of the maximum norm α = ∥uλ ∥∞ of the solution uλ , which is associated with λ, andis expressed as λ = λ(α). In this talk, the case where λ(α) → π 2 , λ(α) → 0 and λ(α) → ∞ as α → ∞ aretreated. In the main theorem, several asymptotic formulas for λ(α) as α → ∞ with the exact second andthird terms are given.
6 梶 木 屋 龍 治 (佐 賀 大 理 工 )Ryuji Kajikiya(Saga Univ.)

Moore–Nehari 方程式の対称および非対称な nodal solution の存在 · · · · 15
Existence of symmetric and asymmetric nodal solutions for the Moore–
Nehari equation.

概 要 We study the existence of symmetric and asymmetric nodal solutions for the Moore–Nehari equation.

Here we call a solution symmetric if it is even or odd. We shall prove the existence of a solution which has
exactly m zeros in the interval (−1, 0) and exactly n zeros in (0, 1) for given nonnegative integers m and n.
7 森
竜 樹 (武 蔵 野 大 工 )久 藤 衡 介 (早 大 理 工 )辻 川
亨 (明大研究・知財)谷
大⋆)四 ツ 谷 晶 二 (龍Tatsuki Mori (Musashino Univ.)
Kousuke Kuto (Waseda Univ.)
Tohru tsujikawa (Meiji Univ.)
Shoji Yotsutani (Ryukoku Univ.⋆)

On the secondary bifurcation curves of a nonlocal Allen–Cahn–Nagumo
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On the secondary bifurcation curves of a nonlocal Allen–Cahn–Nagumo
equation

概 要 We are interested in the Neumann problem of a 1D stationary Allen–Cahn equation with a nonlocal

term. We have obtained the global bifurcation diagram of stationary solutions, which includes the secondary
bifurcation from the odd symmetric solution due to the symmetric breaking eﬀect. Furthermore, we derive
the stability/instability of all symmetric solutions. However, stability/instability of asymmetric solutions
is not clarified. In this talk, we give direction of bifurcation after secondary bifurcation point by using
representation formula of a sheet consisted of all solutions.
14:15〜16:15
8 堀 内 利 郎 (茨 城 大 理 )Toshio Horiuchi (Ibaraki Univ.)

Hardy’s inequalities with non-doubling weights and sharp remainders· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Hardy’s inequalities with non-doubling weights and sharp remainders

概 要 In this talk we shall establish n dimensional weighted Hardy inequalities with non-doubling weightfunctions of the distance function δ(x) to the boundary ∂Ω, where Ω is a C 2 class bounded domain ofRn (n ≥ 1). This work is essentially based on one dimensional weighted Hardy inequalities with one-sided
boundary condition which have sharp remainders. As weights we adopt that may vanish or blow up in
infinite order such as e−1/t and e1/t at t = 0.

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函数方程式論9 濱 本 直 樹 (阪 市 大 数 学 研)
高 橋
太 (阪 市 大 理)

Naoki Hamamoto (Osaka City Univ.)
Futoshi Takahashi (Osaka City Univ.)36

渦無し場に対する Rellich–Hardy 不等式の最良定数 · · · · · · · · · · · · · · · · · 12

The best constant in Rellich–Hardy inequality for curl-free fields

概 要 We report on the Rellich–Hardy inequality with sharp constant for curl-free vector fields. Thisinequality serves as an intermediate between the sharp Hardy– and Rellich–Leray inequalities for curl-freefields, which we found in our previous work on the higher-dimensional and curl-free generalization of thetwo-dimensional case of Costin–Maz’ya’s result.
10 原

宇 信 (北大理)Takanobu Hara (Hokkaido Univ.)

Quasilinear elliptic equations with sub-natural growth terms in boundeddomains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Quasilinear elliptic equations with sub-natural growth terms in boundeddomains

概 要 We consider the existence of positive solutions to weighted quasilinear elliptic diﬀerential equations of

the type−∆p,w u = σuu = 0

q

in Ω,
on ∂Ω

in the sub-natural growth case 0 < q < p − 1, where Ω is a bounded domain in Rn , ∆p,w is a weighted
p-Laplacian, and σ is a Radon measure on Ω. We give criteria for the existence problem. For the proof, weinvestigate various properties of p-superharmonic functions, especially solvability of Dirichlet problems with
non-finite measure data.
11 A. Pomponio (Politecnico di Bari)
渡 辺 達 也 (京 都 産 大 理)

Alessio Pomponio (Politecnico di Bari)
Tatsuya Watanabe(Kyoto Sangyo Univ.)

Ground state solutions for quasilinear scalar field equations arising in
nonlinear optics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Ground state solutions for quasilinear scalar field equations arising in
nonlinear optics

概 要 In this talk, we study a class of quasilinear elliptic equations which appears in nonlinear optics. By

using the mountain pass theorem together with a technique of adding one dimension of space, we prove theexistence of a non-trivial weak solution for general nonlinear terms of Berestycki–Lions’ type. The existenceof a ground state solution is also established under stronger assumptions on the quasilinear term.
12 佐 藤 洋 平 (埼 玉 大 理 工)
柴 田 将 敬 (東 工 大 理)
(Saitama Univ.)
Yohei Sato
Masataka Shibata (Tokyo Tech)

Nonlinear scalar field equations with Berestycki–Lions’ nonlinearity onlarge domains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Nonlinear scalar field equations with Berestycki–Lions’ nonlinearity onlarge domains

概 要 We consider the existence of solutions to −∆u = g(u) in Ω, u ∈ H01 (Ω), where Ω is a suitable large

bounded domain and g satisfies the same conditions as Berestycki–Lions’ conditions. Those conditions ofg are known as “almost suﬃcient and necessary conditions” for the existence of nontrivial solutions to theequations defined in RN . The main diﬃculty to prove the existence of solutions for the bounded domaincase is how to obtain bounded Palais–Smale sequences. To overcome this diﬃculty, we introduce a modified
functional.

最終版: 2020/08/2237函数方程式論13 藤 田 安 啓 (富 山 大 理)
大
理)
浜 向
直 (北
(
山 口 範 和 富山大人間発達)

Yasuhiro Fujita (Univ. of Toyama)
Nao Hamamuki (Hokkaido Univ.)
Norikazu Yanaguchi (Univ. of Toyama)

高木函数を初期値とする Hamilton–Jacobi 方程式における特異性の伝播· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Propagation of singularities in a Hamilton–Jacobi equation with theinitial data of the Takagi function

概 要 We consider the solution to a Hamilton–Jacobi equation with the initial data of the Takagi function,

which is everywhere continuous and nowhere diﬀerentiable. We clarify how singularities of the solution
propagate along generalized characteristics.
14 滝 本 和 広 (広島大先進理工)

Kazuhiro Takimoto (Hiroshima Univ.)

Bernstein type theorem for the parabolic 2-Hessian equation under weakerconditions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Bernstein type theorem for the parabolic 2-Hessian equation under weakerconditions

概 要 In this talk, we deal with the characterization of entire solutions to the parabolic 2-Hessian equationof the form ut = µ(Fk (D2 u)1/2 ) in Rn × (−∞, 0]. We prove that any strictly 2-convex-monotone solutionu = u(x, t) ∈ C 4,2 (Rn × (−∞, 0]) must be a linear function of t and a quadratic polynomial of x, under someassumptions on µ : (0, ∞) → R, some growth conditions on u and the boundedness of 3-Hessian of u frombelow.
16:30〜17:30

2019 年度 (第 18 回) 日本数学会解析学賞受賞特別講演
坂 井 秀 隆 (東 大 数 理) ♭ Painlevé 方程式の世界

Hidetaka Sakai (Univ. of Tokyo)

The world of the Painlevé equations

概 要 More than a century has passed since the Painlevé equations appeared as equations that defines special

functions next to elliptic functions and hypergeometric functions. I have been studying the extension of the
Painlevé equations to discrete dynamical systems or higher dimensional systems. In this talk we will see an
extended world of the Painlevé equations.

9 月 23 日（水）9:30〜11:30
15 藤 原瑠 (明 大 先 端 数 理 )Ryu Fujiwara(Meiji Univ.)

非局所 Allen–Cahn 方程式における不連続な定常解の存在性 · · · · · · · · · · 15

Existence of discontinuous stationary solutions of a nonlocal Allen–Cahn
equation

概 要 We consider stationary solutions of a nonlocal Allen–Cahn equation whose diﬀusion term is definedby using a positive valued integral kernel. We prove that there exist discontinuous stationary solutions if
the diﬀusion coeﬃcient is suﬃciently small. Our result partially extends that of Bates et al., who provedthat there exist discontinuous stationary solutions of a nonlocal Allen–Cahn equation using convolution as
its diﬀusion term.

最終版: 2020/08/22
函数方程式論16 石 井 裕 太 (都 立 大 理)
倉 田 和 浩 (都 立 大 理)

Yuta Ishii (Tokyo Metro. Univ.)
Kazuhiro Kurata (Tokyo Metro. Univ.)

38

メトリックグラフにおける Schnakenberg モデルの多重ピーク解の存在について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Existence of multi-peak stationary solutions to the Schnakenberg model
on metric graphs

概 要 In this talk, we consider the existence of one-peak and two-peak stationary solutions of the Schnaken-berg model with heterogeneity on compact metric graphs. In the one-dimensional interval and nonheterogeneity case, Iron, Wei, and Winter investigated the existence of these solution with symmetry andtheir stability. By using our abstract theorem, we investigate the existence of one-peak solutions andtwo-peak solutions with the same heights of the spikes in the non-heterogeneity case. Moreover, we compare
our results with the results of Wei et al., and reveal the eﬀect of the geometry of the Y -shaped graph to thelocation of concentration points. This is a joint work with Prof. Kazuhiro Kurata.
17 石 井 裕 太 (都 立 大 理)

Yuta Ishii (Tokyo Metro. Univ.)

メトリックグラフにおける Schnakenberg モデルの多重ピーク解の安定性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Stability analysis of multi-peak stationary solutions to the Schnakenberg
model on metric graphs

概 要 In this talk, we consider one-peak and two-peak stationary solutions of the Schnakenberg modelwith heterogeneity on compact metric graphs. We can give the abstract theorem on the stability of thesesolutions for general compact metric graphs under the several assumptions. However, for simplicity, weconcentrate on the Y -shaped metric graph and non-heterogeneity case. The existence of these solutions forgeneral graphs was established by Ishii and Kurata. We establish the stability of these solutions and reveal
the eﬀect of the geometry of the Y -shaped graph to the stability.
18 宮 本 安 人 (東 大 数 理)

Yasuhito Miyamoto (Univ. of Tokyo)

A doubly critical semilinear heat equation in the L1 space · · · · · · · · · · · 10
A doubly critical semilinear heat equation in the L1 space

概 要 We study the existence and nonexistence of a Cauchy problem of the semilinear heat equation in

L1 (RN ): ∂t u = ∆u + |u|p−1 u in RN × (0, T ) and u(x, 0) = ϕ(x) in RN . Here, N ≥ 1, p = 1 + 2/N andϕ ∈ L1 (RN ) is a possibly sign-changing initial function. Since N (p − 1)/2 = 1, the L1 space is scale criticaland this problem is known as a doubly critical case. It is known that a solution does not necessarily exist
for every ϕ ∈ L1 (RN ). In this paper we construct a local-in-time mild solution in L1 (RN ) for a certain ϕ.
We show that there is a nonnegative initial function ϕ0 such that the problem has no nonnegative solution.
We also prove a uniqueness in a certain set of functions which guarantees the uniqueness of the solution
constructed by our method.
()
UCD
19 M. Ghergu(
宮 本 安 人 東 大 数 理)
(UCD)
Marius Ghergu
Yasuhito Miyamoto (Univ. of Tokyo)

Radial single point rupture solutions for a general MEMS model · · · · · 10
Radial single point rupture solutions for a general MEMS model(

概 要 We study the initial value problem: r −(γ−1) r α |u′ |β−1 u′)′

1= f (u)for 0 < r < r0 , u(r) > 0 for

0 < r < r0 and u(0) = 0. Here, γ > α > β ≥ 1, f ∈ C[0, ū) ∩ C (0, ū), f (0) = 0, f (u) > 0 on (0, ū) and f
2

satisfies certain assumptions which include the standard case of pure power nonlinearities encountered in the
study of Micro-Electromechanical Systems (MEMS). We obtain the existence and uniqueness of a solutionu∗ to the above problem, the rate at which it approaches the value zero at the origin and the intersection
number of points with the corresponding regular solutions u( · , a) (with u(0, a) = a) as a → 0. In particular,
these results yield the uniqueness of a radial single point rupture solution and other qualitative properties
for MEMS models. The bifurcation diagram is also investigated.

最終版: 2020/08/2239

函数方程式論20 向 井 晨 人 (東 大 数 理)
関行 宏 (阪 市 大 数 学 研 )Asato Mukai (Univ. of Tokyo)
Yukihiro Seki (Osaka City Univ.)

Refined construction of type II blow-up solutions for a semilinear heat
equation with Joseph–Lundgren supercritical nonlinearity · · · · · · · · · · · 12
Refined construction of type II blow-up solutions for a semilinear heat
equation with Joseph–Lundgren supercritical nonlinearity

概 要 We are concerned with blow-up mechanisms in a heat equation space-dependent nonlinearity:

ut = ∆u + |x|2a up ,x ∈ RN , t > 0,

where p > 1, a > −1 are constants. In the case a = 0, a well-known result due to M. A. Herrero and
J. J. L. Velázquez, C. R. Acad. Sci. Paris Sér. I Math. (1994), states that if N ≥ 11 and p > pJL :=√1 + 4/(N − 4 − 2 N − 1), then there exist radial Type II blow-up solutions. We revisit the idea of theirconstruction and obtain refined estimates for such solutions using the technique developed in recent works
as well as improved arguments on the estimate of the heat semigroup in backward similarity variable.
21 大 西勇 (広 島 大 理 )Isamu Ohnishi (Hiroshima Univ.)

ある種の付属項を持つ半線形放物型偏微分方程式の解の振舞についての発展方程式を用いた特徴付け · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Characterization to behavior of solutions in semi-linear parabolic PDEs
with a certain additional term

概 要 A certain class of semi-linear parabolic PDE with an additional term has been studied here. This

sometimes has a kind of optimal shape of solution, and it is characterized by some mathematical point ofviews of PDE. Today, I will report one of basic validity of foundation of these characterizations by the pointof view of technique of evolution equation theory about its optimality.
13:00〜14:00

特別講演
蘆 田 聡 平 (学 習 院 大 理 )電子のハミルトニアンの固有値の正確な下界評価

Sohei Ashida (Gakushuin Univ.)

Accurate lower bounds for eigenvalues of electronic Hamiltonians

概 要 Electronic Hamiltonians are diﬀerential operators depending on relative positions of nuclei as param-

eters. When we regard an eigenvalue of an electronic Hamiltonian as a function of relative possitions of
nuclei, minimum points correspond to shapes of molecules. Upper bounds for eigenvalues are obtained byvariational methods. However, since only relative energy is relevant to the physical information as minimum
points, physical information can not be obtained by variational methods only. Therefore, lower bounds
are helpful for physical information to be available. In this talk we discuss the various methods for lower
bounds of eigenvalues. In particular, lower bounds for eigenvalues of sums of lower semibounded self-adjoint
operators are introduced. Some computations for systems of one electron and several protons are shown.

9 月 24 日（木）9:30〜11:30
22 井 上 順 平 (早 大 理 工)
久 藤 衡 介 (早 大 理 工 )Jumpei Inoue (Waseda Univ.)
Kousuke Kuto (Waseda Univ.)

拡散ロジスティック方程式における最適棲息分布と L1 非有界な定常解列の存在について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the optimal distribution and the existence of an L1 -unbounded sequence of steady states for the diﬀusive logistic equation

概 要 We discuss a stationary diﬀusive logistic equation on a ball. This talk focuses on an open question thatshowing the upper bound of the ratio of a total population to total resources. In one-dimensional case, Bai–
He–Li (2016) settled that the supremum is equal to 3 by finding a special sequence of diﬀusion coeﬃcientsand carrying functions, and moreover, the first speaker recently obtained profiles of solutions corresponding
to the maximizing sequence. A new question is the following: What happens in higher-dimensional cases?
This talk shows that the supremum is infinite on the spherical symmetry domain.

最終版: 2020/08/22
函数方程式論23 杉 山 由 恵 (阪 大 情 報)
三 浦 正 成 (大 和 大 理 工)
Seungwon Jeong (Seoul Nat. Univ.)

Yoshie Sugiyama (Osaka Univ.)
Masanari Miura (Yamato Univ.)
Seungwon Jeong (Seoul Nat. Univ.)

40

On Hölder continuity of solutions to non-linear diﬀusion equation with
derivative external forces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On Hölder continuity of solutions to non-linear diﬀusion equation with
derivative external forces

概 要 We consider the non-linear diﬀusion equation with derivative external forces. The purpose of our talkis to show the Hölder continuity of solutions to the initial value problem of such an equation.
24 千 代 祐 太 朗 (東 京 理 大 理)
水 上 雅 昭 (東 京 理 大 理)
横 田 智 巳 (東 京 理 大 理)

Yutaro Chiyo (Tokyo Univ. of Sci.)
Masaaki Mizukami(Tokyo Univ. of Sci.)
Tomomi Yokota (Tokyo Univ. of Sci.)

Does the repulsion term really derive boundedness in a chemotaxis system? · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Does the repulsion term really derive boundedness in a chemotaxis system?

概 要 This talk deals with a fully parabolic attraction-repulsion chemotaxis system (1) with signal-dependent

sensitivities and logistic source. The case of constant sensitivities without logistic dampening was studied
by Tao–Wang (2013) under some condition in the two-dimensional setting. The purpose of this talk is toshow global existence and boundedness of classical solutions to the system (1) under several conditions.
25 石 田 祥 子 (千 葉 大 理)
横 田 智 巳 (東 京 理 大 理)
Sachiko Ishida (Chiba Univ.)
Tomomi Yokota (Tokyo Univ. of Sci.)

L1 -保存則をもつ放物型方程式に対する弱解の安定化 · · · · · · · · · · · · · · · · 15
Stabilization of weak solution to parabolic equations with L1 -conservationlaw.

概 要 We consider the initial-boundary value problem for the parabolic equations in divergence form

in a smooth bounded domain under the no-flux boundary condition. In particular, for the problem withdegenerate diﬀusion, it is known that there exists a global-in-time weak solution by the well-known parabolic
theory. We will show that this problem possesses a globally bounded weak solution which approaches asteady state in the large time limit.
26 小 川 卓 克 (東 北 大 理)
黒 木 場 正 城 (室 蘭 工 大 工)

Takayoshi Ogawa (Tohoku Univ.)
Masaki Kurokiba(Muroran Inst. of Tech.)

Keller–Segel 方程式の移流拡散方程式への零緩和時間極限について · · · · 15
Zero relaxation limit for the Keller–Segel equation to the drift-diﬀusion
system概 要 We consider the zero-relaxation limit for the Cauchy problem of the Keller–Segel equations and show

the solution converges to the solution of the corresponding drift-diﬀusion system for all dimension n ≥ 3.
The proof is relies on generalized maximal regularity for the Cauchy problem of the heat equations and thestrong limit in the Bochner–Lebesgue space with the scaling critical exponent is shown.
27 田 中 悠 也 (東 京 理 大 理)
横 田 智 巳 (東 京 理 大 理)

Yuya Tanaka (Tokyo Univ. of Sci.)
Tomomi Yokota (Tokyo Univ. of Sci.)

Does blow-up occur in a Keller–Segel system not only with logistic
source but also with weak chemotactic sensitivity? · · · · · · · · · · · · · · · · · 15
Does blow-up occur in a Keller–Segel system not only with logistic
source but also with weak chemotactic sensitivity?

概 要 This talk deals with blow-up of solutions to a parabolic–elliptic Keller–Segel system with logistic

source and weak chemotactic sensitivity. In a special setting Winkler (2018) found the conditions such thatsolutions blow up in finite time. The purpose of this talk is to give conditions such that there are solutions
which blow up in finite time in the case of weak chemotactic sensitivity.

最終版: 2020/08/2241

函数方程式論28 藤 江 健 太 郎 (東北大RACMaS)()
WIPM
Jie Jiang

Kentarou Fujie (Tohoku Univ.)(WIPM)
Jie Jiang

Comparison methods for a Keller–Segel-type model · · · · · · · · · · · · · · · · 10
Comparison methods for a Keller–Segel-type model

概 要 This talk is concerned with global well-posedness to some chemotaxis system, which was recently

proposed to describe the process of stripe pattern formations via the self-trapping mechanism. In particular,
we consider the case that the motility function is decreasing exponentially. This system shares the same setof equilibria as well as the Lyapunov functional as the Keller–Segel model. In the two-dimensional setting,
we observe a critical-mass phenomenon which is distinct from the well-known fact for the Keller–Segel model.
We prove that the classical solution always exists globally, which remains uniformly-in-time bounded with
arbitrary initial data of subcritical mass. On the contrary, with certain initial data of supercritical mass,
the solution will become unbounded at time infinity.
12:15〜12:35

2020 年度日本数学会解析学賞授賞式

14:15〜16:15
29 鈴 木 将 満 (東 大 数 理)

Masamitsu Suzuki (Univ. of Tokyo)

Local existence and nonexistence for fractional in time weakly coupled
reaction-diﬀusion systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Local existence and nonexistence for fractional in time weakly coupled
reaction-diﬀusion systems

概 要 Let 0 < α < 1 and T > 0. We study the fractional in time weakly coupled reaction-diﬀusion system∂tα u = ∆u + f1 (x, t, v)∂ α v = ∆v + f (x, t, u)2tu(x, t) = v(x, t) = 0u(x, 0) = u (x), v(x, 0) = v (x)00in Ω × (0, T ),in Ω × (0, T ),on ∂Ω × (0, T ),in Ω,

where ∂tα is in the sense of Caputo, and Ω ⊂ RN , N ≥ 1, is a bounded domain with C 2 boundary. We
consider the case where f1 and f2 polynomially grow with respect to v and u, respectively. We obtain
integrability conditions of (u0 , v0 ) which determine the existence/nonexistence of a local in time solution.
30 岩 渕

司 (東 北 大 理 )Tsukasa Iwabuchi (Tohoku Univ.)

Analyticity and large time behavior for the Burgers equation with thecritical dissipation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Analyticity and large time behavior for the Burgers equation with thecritical dissipation

概 要 We study the Cauchy problem of the Burgers equation with the critical dissipation. The solvability

and the global in time regularity are known results. In this talk, we show the following. The first result isthe analyticity in space and time. The second result is the large time behavior of the solution without any
smallness condition on initial data.

最終版: 2020/08/22
函数方程式論工大)31 千 頭昇 (名池 田 正 弘 (理化学研・慶大理工)
谷 口 晃 一 (名 大 多 元 数 理)

Noboru Chikami (Nagoya Inst. of Tech.)
Masahiro Ikeda (RIKEN/Keio Univ.)
Koichi Taniguchi (Nagoya Univ.)

42

Hardy–Hénon 型半線型熱方程式の解の挙動 · · · · · · · · · · · · · · · · · · · · · · · · 10

Behavior of solutions to the energy critical Hardy–Hénon parabolic
equation

概 要 We consider the Cauchy problem for energy critical Hardy–Hénon parabolic equation. Our purpose is

to give a necessary and suﬃcient condition on the initial data below the ground state under which the local
solution in time can be extended globally and its energy decays to zero or it blows up in finite or infinite
time. The proof of dissipation part is based on a concentration compactness, a perturbative result, anda rigidity theorem taking into account existence of the Hardy potential. Especially, our method does notneed backward uniqueness. The proof of blow up part reduces to an argument to an ordinary diﬀerential
inequality for a functional of the localized solution.
大理)
32 西 井 良 徳 (阪砂 川 秀 明 (阪 市 大 理)
寺 下 拓 貴Yoshinori Nishii (Osaka Univ.)
Hideaki Sunagawa (Osaka City Univ.)
Hiroki Terashita

Energy decay for small solutions to semilinear wave equations withweakly dissipative structure · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Energy decay for small solutions to semilinear wave equations withweakly dissipative structure

概 要 In this talk, we present an energy decay result for small data solutions to a class of semilinear wave

equations in two space dimensions possessing weakly dissipative structure relevant to the Agemi condition.
33 杉 山 裕 介 (滋 賀 県 大)

Yusuke Sugiyama (Univ. of Shiga Pref.)Finite time blow-up for parameterized 1D quasilinear wave equations· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Finite time blow-up for parameterized 1D quasilinear wave equations

概 要 We consider the blow-up of solutions to the following parameterized nonlinear wave equation: utt =c(u)2 uxx + λc(u)c′ (u)(ux )2 with the parameter λ ∈ (0, 2]. If λ = 1 and 2, it is known that there exist finite
time blow-up solutions. However, the construction of blow-up solution heavily depends on the structure of
the equation (e.g. the energy conservation law). In this talk, we extend the blow-up result with λ = 1 tothe case with λ ∈ (0, 1] by using a new Lλ/2 estimate.
大理)
34 岡 本葵 (阪(Heriot-Watt Univ.)
J. Forlano

Mamoru Okamoto (Osaka Univ.)
Justin Forlano (Heriot-Watt Univ.)

非線形波動方程式の初期値問題の非適切性について · · · · · · · · · · · · · · · · · 10

On the ill-posedness of the Cauchy problem for the nonlinear wave equation

概 要 We consider the Cauchy problem for the nonlinear wave equation. By using a Fourier analytic

approach, we prove that the nonlinear wave equations experience norm inflation in negative Sobolev spaces.
In particular, we obtain the ill-posedness above the scaling critical regularity for some low dimensional cases.
35 鈴 木貴 (阪 大 M M D S)

Takashi Suzuki (Osaka Univ.)

Minkowski 計量と非定常 Maxwell 方程式の界面消滅 · · · · · · · · · · · · · · · · · 5
Minkowski metric and interface vanishing of non-stationary Maxwell
equation

概 要 We study the interface vanishing of non-stationary Maxwell equation. Even if physical parameters

are discontinuous, singularity of some components of the solution propagates in the light speed across theinterface.

最終版: 2020/08/2243

函数方程式論16:30〜17:30

特別講演
久 藤 衡 介 (早 大 理 工 )Cross-diﬀusion limit in the stationary SKT model

Kousuke Kuto (Waseda Univ.)

Cross-diﬀusion limit in the stationary SKT model

概 要 This talk is concerned with the global bifurcation structure of coexistence steady-states to the

Shigesada–Kawasaki–Teramoto model with cross-diﬀusion (so-called the SKT model). In 1999, Lou–Ni
showed that the asymptotic behavior of coexistence steady-states as one of the cross-diﬀusion terms tends
to infinity can be classified into two types (the segregation type and the shrink type). For the segregation
type, the set of solutions to the corresponding limiting system (the 1st limiting system) has been revealed
mainly by Lou–Ni–Yotsutani. This talk focuses on the shrink type and studies the corresponding limiting
system (the 2nd limiting system). We obtain the global bifurcation structure of positive solutions to the 2ndlimiting system. Furthermore, by the perturbation of solutions of two limiting systems, we construct thebifurcation branch of coexistence steady-states to the SKT model in a case when one of the cross-diﬀusion
terms is suﬃciently large.

9 月 25 日（金）9:30〜11:30
36 伊 藤 弘 道 (東 京 理 大 理)
V. A. Kovtunenko(Univ. of Graz・Lavrentyev Inst. of Hydrodynamics)
K. R. Rajagopal (Texas A&M Univ.)

Hiromichi Itou (Tokyo Univ. of Sci.)
Victor A. Kovtunenko(Univ. of Graz/Lavrentyev Inst. of Hydrodynamics)
Kumbakonam R. Rajagopal(Texas A&M Univ.)

On flat-punch indentation problems within the context of linearizedviscoelasticity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On flat-punch indentation problems within the context of linearizedviscoelasticity

概 要 In this talk, the indentation of a flat-ended cylindrical rigid punch into a viscoelastic half-space isstudied. This is closely related to the Boussinesq problem for finding the deformation in the case of aconcentrated load applied on the plane boundary, by passing to the limit as the punch radius tends to zero.
The indentation test has technological importance because of the ubiquitous use to determine the material
properties of a body. For this problem, we assume a linear viscoelastic model wherein the linearized strain
is expressed as a function of the stress. However, this expression is not invertible. Then, without use of acorrespondence principle between the solutions in linearized elasticity and linear viscoelasticity, distributionof the displacement and the stress fields is obtained in the closed form, based on the Papkovich–Neuber
representation in potential theory and use of the Fourier–Bessel transform for axisymmetric bodies.
37 牧 野

哲 (山

口

大⋆)

Tetu Makino (Yamaguchi Univ.

⋆)

気体星の断熱的非動径振動における g-モードの存在について · · · · · · · · · 15

On the existence of g-modes in adiabatic non-radial oscillations of gaseousstars

概 要 We discuss adiabatic no-radial oscillations of a gaseous star around a spherically symmetric equilibrium

which touches the vacuum at a finite radius. When the square of the Brunt–Vaisala frequency on the
background equilibrium has a positive minimum, then we can prove the existence of a sequence of positive
eigenvalues accumulating to 0 for the linearized integro-diﬀerential operator which governs the perturbations
described by Lagrangian coordinate. This is a mathematically rigorous proof of the existence of so called
g-modes discussed in the astero- or helio-seismology.

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函数方程式論44

38 佐 藤 拓 也 (東 北 大 理) ♭ L2 -decay for the one dimensional dissipative nonlinear Schrödinger equa小 川 卓 克 (東 北 大 理) tion in a critical exponent · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Takuya Sato (Tohoku Univ.)
Takayoshi Ogawa (Tohoku Univ.)

L2 -decay for the one dimensional dissipative nonlinear Schrödinger equation in a critical exponent

概 要 We consider the Cauchy problem for the dissipative nonlinear Schrödinger equation with cubic

nonlinearities in one space dimension. For the dissipative nonlinear term, the cubic nonlinearity in one
space dimension is the threshold to exhibit the L2 -decay of solutions. We prove the existence for the global
analytic solution and show the L2 -decay of the solution in the critical exponent.
39 Chunhua Li ( Yanbian Univ. )大理)
西 井 良 徳 (阪佐 川 侑 司砂 川 秀 明 (阪 市 大 理)
Chunhua Li (Yanbian Univ.)
Yoshinori Nishii (Osaka Univ.)
Yuji Sagawa
Hideaki Sunagawa (Osaka City Univ.)

Large time asymptotics for a cubic nonlinear Schrödinger system in one
space dimension, II · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Large time asymptotics for a cubic nonlinear Schrödinger system in one
space dimension, II

概 要 We study the Cauchy problem for the two-component system of cubic nonlinear Schrödinger equations

in one space dimension. We provide criteria for large time decay or non-decay in L2 of the small amplitude
solutions in terms of the Fourier transforms of the initial data.
40 浜 野大 (埼 玉 大 理 工)
池 田 正 弘 (理化学研・慶大理工)

Masaru Hamano (Saitama Univ.)
Masahiro Ikeda (RIKEN/Keio Univ.)

逆冪乗型ポテンシャルを持つ非線形シュレディンガー方程式の初期値の条件の同値性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

For equivalence of conditions on initial data to the nonlinear Schrödinger
equation with an inverse power potential

概 要 In this talk, we consider the nonlinear Schrödinger equation with a repulsive inverse power potential.

First, we introduce minimization problems for the ground state to the NLS equation. Then, we deal withinitial data, whose action is less than that of the ground state without the potential. We prove some global
well-posedness results and some blow-up results. In addition, focusing on the time behavior of solutions to
the NLS equation, we give equivalence of some conditions on the initial data.
41 田 中 智 之 (名 大 多 元 数 理)
平 山 浩 之(宮崎大テニュアトラック推進機構)
池 田 正 弘(理化学研 AIP・慶大理工)

Tomoyuki Tanaka (Nagoya Univ.)
Hiroyuki Hirayama (Univ. of Miyazaki)
Masahiro Ikeda (RIKEN/Keio Univ.)

Well-posedness for the fourth-order Schrödinger equation with third order derivative nonlinearities · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Well-posedness for the fourth-order Schrödinger equation with third order derivative nonlinearities

概 要 We study the Cauchy problem to the semilinear fourth-order Schrödinger equations. The purposeof this talk is to prove well-posedness in the lower order Sobolev space H s (R) or with more general
nonlinearities than previous results. Our proof of the main results is based on the contraction mapping
principle on a suitable function space employed by D. Pornnopparath (2018). To obtain the key linear andbilinear estimates, we construct a suitable decomposition of the Duhamel term introduced by I. Bejenaru,
A. D. Ionescu, C. E. Kenig, and D. Tataru (2011).

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函数方程式論42 山 崎 陽 平 (広 島 大 理)

Yohei Yamazaki (Hiroshima Univ.)

Zakharov–Kuznetsov 方程式の臨界速度を持つ線状進行波周りの中心安定多様体について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10Center stable manifolds around line solitary waves of the Zakharov–
Kuznetsov equation with critical speed

概 要 In this talk, we consider center stable manifolds around unstable line solitary waves of the Zakharov–

Kuznetsov equation on two dimensional cylindrical spaces. In the previous result, center stable manifolds
around unstable line solitary waves have been constructed without critical speed c ∈ {4n2 /5L2 ; n ∈ Z, n > 1}.
Since the linearized operator around line solitary waves with critical speed is degenerate, we prove thestability condition of the center stable manifold for critical speed by applying to the estimate of 4th orderterm of a Lyapunov function.
14:15〜16:15
43 清 水 雄 貴 (京Yuuki Shimizu

大理)(Kyoto Univ.)曲面上の Euler 方程式のカレント値弱解とその応用 · · · · · · · · · · · · · · · · · 15

A current-valued solution of the Euler equations on surfaces and its
applications

概 要 We provide a characterization of point vortex dynamics in a background field on general curved

surfaces as a current-valued solution of the Euler equations. Introducing a weak formulation of the Euler
equations on a surface in the space of currents, we discuss universality and existence of point vortex dynamics
in a background field in certain current-valued solutions.
44 仲 尾 光 平 (長 野 大 非 常 勤)
Kohei Nakao(Nagano Univ.)

On time-periodic solutions to the Boussinesq equations in exterior domains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On time-periodic solutions to the Boussinesq equations in exterior domains

概 要 We construct time-periodic solutions to the Boussinesq equations in a three-dimensional exterior

domain. To this end, we estimate the L1 norm of buoyancy, and give some estimates of the heat semigroupin the Lorentz space.
45 岡 部 考 宏 (阪 大 基 礎 工)
L. Brandolese ( Univ. Lyon 1 )Takahiro Okabe (Osaka Univ.)
Lorenzo Brandolese (Univ. Lyon 1)

Annihilation of slow-decay factors of the Navier–Stokes flow by the external force · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Annihilation of slow-decay factors of the Navier–Stokes flow by the external force

概 要 We consider the incompressible Navier–Stokes equations on the whole space. We derive rapid time

decay of the energy of the Naiver–Stokes flow beyond the optimal decay rate by the eﬀect of the external
force. More precisely, for every (small) initial data we find a external force and the associated solution
which decays rapidly. Moreover we see that we can take force which has a compact support in space-time
region.

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函数方程式論46 橋 本 伊 都 子(金沢大理工・阪市大数学研)
松 村 昭 孝 (阪 大 情 報)
Itsuko Hashimoto(Kanazawa Univ./Osaka City Univ.)
Akitaka Matsumura (Osaka Univ.)46

圧縮性 Navier–Stokes 方程式の球対称定常解 の存在について · · · · · · · · · 10

Existence of radially symmetric stationary solutions for the compressible
Navier–Stokes equation

概 要 The present paper is concerned with the existence of radially symmetric stationary solutions forexterior problems to the compressible Navier–Stokes equation, describing the motion of viscous barotropic
gas without external forces, where boundary and far field data are prescribed. For both inflow and outflow
problems, the existence of a unique radially stationary solution is shown in a suitably small neighborhoodof the far field state. The estimates of algebraic decay rate toward the far field state are also obtained.
Furthermore, it is shown that the boundary layer of the density appears as the velocity data tend to zero in
the inflow problem, but not in the outflow problem.
工大)47 鈴 木 政 尋 (名高 山 正 宏 (慶 大 理 工)

Masahiro Suzuki (Nagoya Inst. of Tech.)
Masahiro Takayama (Keio Univ.)

摂動半空間における Euler–Poisson 方程式の定常解 · · · · · · · · · · · · · · · · · 15

Stationary solutions to the Euler–Poisson equations in a perturbed halfspace

概 要 The purpose of this talk is to mathematically investigate the formation of a plasma sheath near thesurface of walls immersed in a plasma, and to analyze qualitative information of such a sheath layer. In thecase of planar wall, Bohm proposed a criterion on the velocity of the positive ion for the formation of sheath,and several works gave its mathematical validation. In this talk, we study the existence and asymptotic
stability of stationary solutions for the Euler–Poisson equations in a domain of which boundary is drawn
by a graph. The existence and stability theorems are shown by assuming that the velocity of the positive
ion satisfies the Bohm criterion at infinite distance. What most interests us in these theorems is that thecriterion together with a necessary condition guarantees the formation of sheaths.
工大)48 鈴 木 政 尋 (名Katherine Zhiyuan Zhang( Brown Univ. )Masahiro Suzuki (Nagoya Inst. of Tech.)Katherine Zhiyuan Zhang(Brown Univ.)

摂動半空間における Navier–Stokes 方程式の定常解 · · · · · · · · · · · · · · · · · 15

Stationary solutions to the Navier–Stokes equations in a perturbed halfspace

概 要 We consider the compressible Navier–Stokes equations in a perturbed half-space with an outflow

boundary condition as well as the supersonic condition. For a half-space, it has been known that a certain
planar stationary solution exists and it is time-asymptotically stable. The planar stationary solution is
independent of the tangential directions and its velocities of the tangential directions are zero. In thispaper, we show the unique existence of stationary solutions for the perturbed half-space. The feature of ourwork is that our stationary solution depends on all directions and has multidirectional flow. Furthermore,
we also prove the asymptotic stability of this stationary solution.

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函数方程式論49 石 垣 祐 輔 (東 工 大 理)
Yusuke Ishigaki (Tokyo Tech)Diﬀusion wave phenomena and Lp decay estimates of solutions of compressible viscoelastic system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Diﬀusion wave phenomena and Lp decay estimates of solutions of compressible viscoelastic system

概 要 We consider the system of equations describing motion of compressible viscoelastic fluids in three

dimensional whole space. We investigate the large time behavior of solutions around a motionless state,
and obtain the Lp decay estimates of solutions for 1 < p ≤ ∞, provided that the initial data is suﬃciently
close to the motionless state. In addition, we clarify the diﬀusion wave phenomena caused by interaction of
three properties; sound wave, viscous diﬀusion and elastic shear wave.
16:30〜17:30

特別講演
瀬 片 純 市 (九 大 数 理 )Jun-ichi Segata (Kyushu Univ.)

デルタポテンシャルをもつ非線形シュレディンガー方程式の解の長時間
挙動Long time behavior of solution to the nonlinear Schrödinger equation
with delta potential

概 要 We summarize recent progress on long time behavior of solution to the initial-value problem for the

one dimensional nonlinear Schrödinger equation with a delta potential. We first consider the case where
potential is repulsive and prove that small global solutions decay in L∞ and exhibit (modified) scattering.
Next we mention the case where potential is attractive and prove that for suﬃciently small initial data, thecorresponding global solution decomposes into a small solitary wave plus a radiation term that decays andscatters as t → ∞. In particular, we establish the asymptotic stability of the family of small solitary waves.

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実

函

数

48

論

9 月 24 日（木）10:00〜11:55(埼 玉 大 理 工)
1 N. Bez
中 村 昌 平 (埼 玉 大 理 工)
(Saitama Univ.)
Neal Bez
Shohei Nakamura (Saitama Univ.)

Inverse Brascamp–Lieb inequalities via the heat equation · · · · · · · · · · · 15
Inverse Brascamp–Lieb inequalities via the heat equation

概 要 Vaguely speaking, our interest in this talk is about the diﬀerence between two methodology, that is,

the mass-transport method and the semigroup interpolation method, especially the heat flow monotonicity.
To this question, we consider the inverse Brascamp–Lieb inequality which generalises the sharp forward
and reverse Young’s inequality, gaussian hypercontractivity for the Ornstein–Uhlenbeck semigroup, as wellas Prékopa–Leindler inequality, and hence the Brunn–Minkowski inequality. This was recently establishedby Barthe–Wolﬀ employing the mass-transport method. We will report that the heat flow monotonicity
approach enables us to further generalise and somehow improve the inverse Brascamp–Lieb inequality. Our
generalised inequalities unify most of inequalities related to the theory of the Brascamp–Lieb inequality.
This talk is based on the joint work with Professor Neal Bez.
2 本 田 あ お い (九 工 大 情 報 工)
福 田 亮 治 (大 分 大 理 工)
岡 崎 悦 明 (ファジィシステム研)

Aoi Honda (Kyushu Inst. of Tech.)(Oita Univ.)
Ryoji Fukuda
Yoshiaki Okazaki(Fuzzy Logic Systems Inst.)

k 次加法的単調測度の非離散への一般化 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Generalization of k-order additive monotone measure for nondiscretespace

概 要 The k-order additivity which is one of the main concepts for analyzing non-additivbe measure isconsidered. We introduce a generalization of the concept of the Möbius transform, and define the k-order
additivity for nondiscrete monotone measure space with this. We show the the validity of this definitionand essential properties of k-oider additivitiy. In addition we give several concrete examples of non-discrete
k-order additive measure.
3 厚 芝 幸 子 (東京女大現代教養)
Sachiko Atsushiba(Tokyo Woman’s Christian Univ.)

Fixed points and convergence of orbits of nonexpansive semigroups · · · 15
Fixed points and convergence of orbits of nonexpansive semigroups

概 要 In this talk, we prove some fixed point results for generalized contractions in Banach spaces. We

prove convergence theorems for generalized contractions. We also study the asymptotic behavior of orbits
of nonexpansive semigroups with no common fixed points in the interior of their domains.
4 冨 澤 佑 季 乃 (新 潟 工 大 工)
Yukino Tomizawa(Niigata Inst. of Tech.)

完備 Busemann 空間の一様凸性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Uniform convexity of complete Busemann spaces

概 要 Some distance space which are not linear spaces have properties such that the generalization ofproperties in linear spaces. The purpose is to elucidate what geometrical properties exist in the spaces. wereport some geometric properties of complete Busemann spaces with uniform convexity.

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49

実函数論

♭
5 池 田 正 弘
解析的な正定値関数に付随する再生核 Hilbert 空間上の合成作用素の有界(理化学研 AIP・慶大理工) 性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
石 川
勲
(愛媛大データサイエンスセンター)
澤 野 嘉 宏 (中 大 理 工 )Masahiro Ikeda (RIKEN/Keio Univ.)(Ehime Univ.)
Isao Ishikawa
Yoshihiro Sawano (Chuo Univ.)

Composition operators on reproducing kernel Hilbert spaces with analytic positive definite functions

概 要 Composition operators have been extensively studied in complex analysis, and recently, they havebeen utilized in engineering and machine learning. Here, we focus on composition operators associated withmaps in Euclidean spaces that are on reproducing kernel Hilbert spaces with respect to analytic positive
definite functions, and prove the maps are aﬃne if the composition operators are bounded. Our result
covers composition operators on Paley–Wiener spaces and reproducing kernel spaces with respect to theGaussian kernel on Rd , widely used in the context of engineering.
6 波多野修也(中大理工・理化学研 AIP)
池 田 正 弘 (理 化 学 研 AIP)石 川勲
(愛媛大データサイエンスセンター)
澤 野 嘉 宏 (中 大 理 工 )Naoya Hatano (Chuo Univ./RIKEN)(RIKEN)
Masahiro Ikeda(
Ehime
Univ.)
Isao Ishikawa
Yoshihiro Sawano (Chuo Univ.)

モレー空間における合成作用素の有界性 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Boundedness of composition operators on Morrey spaces

概 要 Composition operator is also said Koopman operator and is used well in the engineering field. Morrey

space is a generalization of Lebesgue space, which is introduced in 1938, and attract attention recently. Our
goal of the investigation is to show the necessary and suﬃcient condition of boundedness of composition
opearators on Morrey spaces. It is well known the necessary and suﬃcient condition of boundedness ofcomposition operators on Lebesgue spaces from long ago. In our investigation, we succeeded getting out
the detailed informations of composing maps from the boundedness on Morrey spaces. The main result,which is a suﬃcient condition of boundedness on Morrey spaces, is not possible to consider by only using
Lebsegue spaces.
7 宮 崎 洋 一 (日大歯)Yoichi Miyazaki (Nihon Univ.)

村松の積分公式による BMO 項を含む Gagliardo–Nirenberg の不等式の証明 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A proof of the Gagliardo–Nirenberg inequality with BMO term via Muramatu’s integral formula1−k/m

概 要 It is known that the Gagliardo–Nirenberg inequality ∥∇k f ∥Lr ≤ C∥f ∥L∞k/m∥∇m f ∥Lp

with r =mp/k, 1 < p < ∞, 1 ≤ k < m can be improved by replacing the L∞ norm with the BM O norm. We givea short proof of this refined inequality, using Muramatu’s integral formula. Compared with the proof given
by Strzelecki [Bull. London Math. Soc 38 (2006), 294–300], we do not need the duality of the Hardy space
and the BMO space. We also consider the case where ∥∇m f ∥BM O is concerned.

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50

14:15〜14:45
8 川 澄 亮 太
Ryota Kawasumi

Weak-weak boundedness of commutators of generalized fractional integral operators with functions in Campanato spaces · · · · · · · · · · · · · · · · · 15
Weak-weak boundedness of commutators of generalized fractional integral operators with functions in Campanato spaces

概 要 We consider the commutator [b, Iρ ] on weak Orlicz–Morrey spaces, where Iρ is a generalized fractional

integral operator and b is a function in generalized Campanato spaces. We show the boundedness froma weak Orlicz–Morrey space to another weak Orlicz–Morrey space. Weak Orlicz–Morrey spaces containweak Lp spaces, weak Orlicz spaces and weak generalized Morrey spaces as special cases. Hence we get the
weak-weak boundedness of these function spaces as corollaries of our result, which are also new results.
9 川 澄 亮 太
中 井 英 一 (茨 城 大 理)石明 磊 (茨 城 大 理 工)
Ryota Kawasumi(Ibaraki Univ.)
Eiichi Nakai(Ibaraki Univ.)
Minglei Shi

Generalized fractional integral and maximal operators on Orlicz–Morrey
and weak Orlicz–Morrey spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Generalized fractional integral and maximal operators on Orlicz–Morrey
and weak Orlicz–Morrey spaces

概 要 We consider the generalized fractional integral operator Iρ and the generalized fractional maximal

operator Mρ . We give necessary and suﬃcient conditions for the boundedness of Iρ and Mρ on Orlicz–Morrey
and weak Orlicz–Morrey spaces. Orlicz–Morrey spaces contain Lp spaces, Orlicz spaces and generalized
Morrey spaces as special cases. Hence we get necessary and suﬃcient conditions for the boundedness of Iρ
and Mρ on these function spaces as corollaries.
15:00〜16:00
貞 末

特別講演
岳 (大阪教育大数学教育)

Gaku Sadasue (Osaka Kyoiku Univ.)

Martingale 空間と, 分数べき積分
Martingale spaces and fractional integrals

概 要 In this talk, we give definitions of several martingale spaces, and study the boundedness of martingale

transforms on these spaces. We especially study a special class of martingale transforms called fractional
integrals.

9 月 25 日（金）9:45〜12:00
10 小 杉 千 春 (日 本 女 大 理)
愛 木 豊 彦 (日 本 女 大 理)

Chiharu Kosugi (Japan Women’s Univ.)
Toyohiko Aiki (Japan Women’s Univ.)

平面上において弾性体の伸縮運動を表現する初期値境界値問題の弱解の一意性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Uniqueness of weak solutions to initial and boundary value problems
representing motion of the elastic material on plane

概 要 In this talk we consider uniqueness of weak solutions to an initial boundary value problem for beam

equations. This problem represents motion of the elastic material (for example rubber rings), and is to finda closed curve defined on the closed interval [0,1]. We note that the strain is given by a nonlinear function of
the derivative of the unknown function so that we define a solution in a weak formulation. The existence ofthe solution was already shown. The aim of this talk is to prove a theorem on uniqueness of weak solutions.
In our proof by applying the dual equation method we establish the uniqueness of weak solutions.

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51

実函数論

11 奥 村 真 善 美 (阪 大 情 報)

Makoto Okumura (Osaka Univ.)

総質量保存則を持つ動的境界条件下の Cahn–Hilliard 方程式に対する構
造保存スキーム · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A structure-preserving scheme for the Cahn–Hilliard equation with dynamic boundary conditions which has the total mass conservation

概 要 We propose a structure-preserving scheme for the GMS model by using the discrete variational

derivative method (DVDM). In the model, two characteristic properties hold. One is the total massconservation, which means that the sum of the mass in bulk and on the boundary is conserved. The other isthe total energy dissipation, which represents the sum of energy in bulk and on the boundary decrease. In
this study, we design a finite diﬀerence scheme for the GMS model so that the scheme inherits the properties
from the original problem in a discrete sense. In this talk, we focus on the existence and uniqueness of thesolution for the scheme.
12 水 上 雅 昭 (東 京 理 大 理)
Masaaki Mizukami(Tokyo Univ. of Sci.)

Uniform-in-time estimates for solutions of a chemotaxis-competition
model and those of the Lotka–Volterra competition model · · · · · · · · · · · 15
Uniform-in-time estimates for solutions of a chemotaxis-competition
model and those of the Lotka–Volterra competition model

概 要 This work is concerned with the question that “how far does small chemotactic interaction perturb the

Lotka–Volterra competition dynamics?”. A two-species chemotaxis-competition model was studied by e.g.,
Bai–Winkler (2016) and Lin–Mu–Wang (2015). However, there are still many open problems about the twospecies chemotaxis-competition model. On the other hand, the Lotka–Volterra competition model has beenstudied extensively. Thus the development of this work will enable us to see new properties of solutions forthe chemotaxis system. The main result of this talk gives uniform-in-time error estimates between solutionsof the two-species chemotaxis-competition system and those of the Lotka–Volterra competition model.
13 都 築寛 (広島修道大経済)

Yutaka Tsuzuki(Hiroshima Shudo Univ.)

Existence for initial–boundary value problems for Vlasov–Poisson equations with angle error in magnetic field · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Existence for initial–boundary value problems for Vlasov–Poisson equations with angle error in magnetic field

概 要 We deal with initial–boundary problems for Vlasov–Poisson systems in a half-space.

In 2013,

Skubachevskii provides local-in-time solvability to the system. Furthermore, in 2017, existence resultwith weaker condition were also obtained where the magnetic force is horizontal to the wall. This talkprovides another result for the equation where the magnetic force has angle error in the vertical direction
and depending on the first element of the spatial variable.
14 久 保 田 翔 大 (千葉大融合理工)白 川
健 (千 葉 大 教 育 )Shodai Kubota (Chiba Univ.)
Ken Shirakawa (Chiba Univ.)

一般多次元における Kobayashi–Warren–Carter システムに対する最適制
御問題 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Optimal control problems for multidimensional systems of Kobayashi–
Warren–Carter type

概 要 We consider optimal control problems for state problems of multidimensional systems. Each state

problem is denoted by (S)ε , with ε > 0, and is based on the phase-field model of grain boundary motion.
M

In this regard, each optimal control problem is denoted by (OP)ε , with ε > 0 and M > 0, and it isM

prescribed as a minimization problem of a cost function. Additionally, the problems (S)ε and (OP)ε aresupposed to admit limiting profiles as ε ↓ 0, and then, the limiting problems are supposed to contain nolittle singularities. The main interest is in the case when ε > 0 (regular case), and the mathematical results
concerned with: (A) the existence of the optimal control when ε > 0; (B) the necessary condition for the
regular optimal control; (C) limiting observation as ε ↓ 0; will be reported as the main theorems of this talk.

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実函数論

15 深 尾 武 史 (京 都 教 育 大)
( Univ. of Pavia )P. Colli

Takeshi Fukao (Kyoto Univ. of Edu.)
Pierluigi Colli (Univ. of Pavia)

52

動的境界条件下での Cahn–Hilliard 方程式系に対する境界拡散項の消滅について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Vanishing diﬀusion in a dynamic boundary condition for the Cahn–
Hilliard equation

概 要 In this talk, we will discuss the Cahn–Hilliard equation with a dynamic boundary condition of Allen–

Cahn type. We focus on the analysis of the surface diﬀusion on the dynamic boundary condition. By theasymptotic analysis, we can expect that the solution with the surface diﬀusion converges to the one ofwithout the surface diﬀusion in a sense. The role of the surface diﬀusion will be expressed by means of theclasses of the solutions.
16 白 川渡 邉健 (千 葉 大 教 育)紘 (大 分 大 理 工)

Ken Shirakawa (Chiba Univ.)
Hiroshi Watanabe (Oita Univ.)

Suﬃcient condition for the existence of one-dimensional crystalline solution of the Kobayashi–Warren–Carter type system · · · · · · · · · · · · · · · · 15
Suﬃcient condition for the existence of one-dimensional crystalline solution of the Kobayashi–Warren–Carter type system

概 要 This summary is the same with that for the presentation at the last MSJ Spring Meeting 2020. In thistalk, we consider a one-dimensional Kobayashi–Warren–Carter type system, which is based on a phase-fieldmodel of grain boundary motion. This talk corresponds to a continuation of the last presentation at MSJ
Spring Meeting 2019 (Tokyo), which was concerned with the uniqueness of special kind of solution, named“crystalline solution”. On this basis, we here focus on the existence issue of crystalline solution. Throughthe precise observations for solutions to a time-discretization scheme, a class of structural conditions for the
initial data will be presented as the suﬃcient condition for the existence of crystalline solution.
17 山 崎 教 昭 (神 奈 川 大 工)葉大⋆)剣 持 信 幸 (千白 川
健 (千 葉 大 教 育)

Noriaki Yamazaki (Kanagawa Univ.)
Nobuyuki Kenmochi (Chiba Univ.⋆)
Ken Shirakawa (Chiba Univ.)

Control of parameter-dependent evolution equations governed by timedependent subdiﬀerentials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Control of parameter-dependent evolution equations governed by timedependent subdiﬀerentials

概 要 We consider nonlinear parameter-dependent evolution equations governed by double time-dependent

subdiﬀerentils in uniformly convex Banach spaces. In this talk, we investigate singular optimal control
problems for doubly nonlinear parameter-dependent evolution state equations. Then, we show the existenceof an optimal control for our problem.
14:15〜15:15
18 熊 崎 耕 太 (長 崎 大 教 育) ♭ 水分膨張を表すある 1 次元自由境界問題の時間大域的な解の挙動について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Kota Kumazaki (Nagasaki Univ.)

Large time behavior of a solution of a one-dimensional free boundary
problem describing water swelling概 要 In this talk, we consider a mathematical model describing swelling of a pocket of water in porous

materials. Our problem is posed on a halfline with a moving boundary at one of the ends, and the moving
boundary conditions encode the swelling mechanism, while a diﬀusion equation is responsible for providing
water content for the swelling to take place. Recently, we investigate the large time behavior of the freeboundary position and see that the moving interfaces grows indefinitely unless the production term byHenry’s law has a certain decay in time. In this talk, we discuss the existence and uniqueness, large time
behavior of a solution to our problem.

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53

実函数論

19 内 田俊 (大 分 大 理 工 )Shun Uchida(Oita Univ.)

Solvability of doubly nonlinear parabolic equations with p-Laplacian · · 15
Solvability of doubly nonlinear parabolic equations with p-Laplacian

概 要 We are concerned with the initial boundary value problem of ∂t β(u) − ∆p u ∋ f in a bounded domain

with the homogeneous Dirichlet boundary condition, where β is (multi-valued) maximal monotone graph in
R and ∆p u := ∇ · (|∇u|p−2 ∇u). The main purpose of this talk is to show the existence of solutions withoutboundedness, growth order, and coercivity conditions of β.
20 渡 邉紘 (大 分 大 理 工 )Hiroshi Watanabe (Oita Univ.)

放物型・双曲型単独保存則に対する複数の不連続点を持つ進行波 · · · · · · 15

Traveling waves with multiple points of discontinuities to scalar parabolichyperbolic conservation laws

概 要 We consider one-dimensional Cauchy problems (CP) for scalar parabolic-hyperbolic conservation laws.

The equation is regarded as a linear combination of the hyperbolic conservation laws and the porous
medium type equations. Thus, this equation has both properties of hyperbolic equations and those ofparabolic equations. Accordingly, it is diﬃcult to investigate the behavior of solutions to (CP). In thistalk, we construct traveling waves with multiple points of discontinuities and discuss the properties of them.
Moreover, we show the constructed traveling waves are entropy solutions to (CP).
21 松 本 敏 隆 (静 岡 大 理)岡裕 和 (茨 城 大 工 )田 中 直 樹 (静 岡 大 理 )Toshitaka Matsumoto (Shizuoka Univ.)
Hirokazu Oka (Ibaraki Univ.)
Naoki Tanaka (Shizuoka Univ.)

Carathéodory 条件を満たす準線形作用素に支配される発展方程式に対する適切性と近似可解性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Well-posedness and approximation solvability for evolution equations
governed by quasilinear operators satisfying Carathéodory’s conditions

概 要 Evolution equations governed by quasilinear operators satisfying Carathéodory’s conditions are stud-

ied. Time-local and time-global well-posedness results as well as approximation solvability results are
given.
15:30〜16:30

特別講演

高 棹 圭 介(京大理・京大白眉センター)

フェイズフィールド法による外力項付き平均曲率流方程式の弱解の存在について

Keisuke Takasao(Kyoto Univ. / Kyoto Univ.)

On the existence of the weak solution for the mean curvature flow with
forcing term via the phase field method

概 要 We study the mean curvature flow with given non-smooth forcing term g. In 1993, Ilmanen proved

the existence of the Brakke flow without forcing term, by using the phase field method. Generally, the mostdiﬃcult part of the proof of the existence theorem is the estimate of the positive part of the discrepancy
measure. To solve the problem, Ilmanen showed the non-positivity of the discrepancy measure via themaximum principle. However, in the case of g ̸= 0, the property does not hold for the usual phase field
method of the problem. In this talk, we explain a new modified Allen–Cahn equation which satisfies thenon-positivity of the discrepancy measure, and we prove the global existence of the weak solution for themean curvature flow with forcing term in suitable Sobolev spaces.

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函数解析学

函

数

解

析

54

学

9 月 22 日（火）10:00〜11:45
1 井 上

寛 (第 一 薬 大)Hiroshi Inoue (Daiichi Univ. of Pharm.)

双準直交系から構成される非自己共役ハミルトニアンと準線形形式に関する研究 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Non-self-adjoint hamiltonians defined by biorthogonal sequences andsesquilinear forms

概 要 In this talk, we introduce a theory of sesquilinear forms with respect to non-self-adjoint hamiltonian andits physical operators. In particular, we discuss some features of non-self-adjoint operators and sesquilinear
forms which are defined starting from biorthogonal sequences which are not Riesz bases, generalized Riesz
systems, D-quasi bases and (D, E)-quasi bases.
2 清 瀬周
足 立 匡 義 (京 大 人 間 環 境)
Amane Kiyose
Tadayoshi Adachi (Kyoto Univ.)

Floquet ハミルトニアンに対する Mourre 評価について · · · · · · · · · · · · · · 15
On the Mourre estimates for Floquet Hamiltonians

概 要 We introduce a new conjugate operator for the Floquet Hamiltonian associated with a Schrödinger

operator with time-periodic potentials. Although Yokoyama (1998) already obtained a conjugate operator
for the Floquet Hamiltonian, there was a diﬃculty that it won’t aﬀord extensions to the many-body systems.
Here we introduce our new conjugate operator which suggests such extensions. Actually, combining our
results and Yokoyama’s, Adachi recently constructed a conjugate operator for three-body systems.
3 板 倉 恭 平
(立命館大総合科学技術研究機構)

Kyohei Itakura (Ritsumeikan Univ.)

Stationary scattering theory for repulsive Hamiltonians · · · · · · · · · · · · · 15
Stationary scattering theory for repulsive Hamiltonians

概 要 We investigate stationary scattering theory for Hamiltonians with spherically symmetric repulsive

potential. For such Hmailtonians we already studied spectral theory and obtained some results for generalized eigenfunctions and resolvents on proper spaces. To construct stationary scattering theory radiation
condition bounds for limiting resolvents play a crucial role. We are going to talk about construction of
stationary wave matrices and its properties.
4 髙 江 洲 俊 光 (群 馬 大 理 工)

Toshimitsu Takaesu (Gunma Univ.)

準相対論的な粒子と Klein–Gordon 場が相互作用する系の紫外切断を外すスケーリング極限について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Scaling limits with a removal of ultraviolet cutoﬀs for the system ofsemi-relativistic particles coupled to a Klein–Gordon field

概 要 We consider the system of semi-relativistic particles coupled to a Klein–Gordon field. A scaled total

Hamiltonian for the system is defined on a tensor product of a square-integrable function space and a boson
Fock space. We consider the strong resolvent limit of a renormalized Hamiltonian, which is defined bysubtracting a divergent term from the scaled total Hamiltonian. By an abstract scaling limit theory and aunitary transformation, eﬀective potentials of particles are derived.

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55

函数解析学

5 岩 田 順 敬 (関西大化学生命工)
Yoritaka Iwata (Kansai Univ.)

抽象 Miura 変換の高階発展方程式論への応用 · · · · · · · · · · · · · · · · · · · · · · · 15

Application of abstract Miura transform to higher order abstract evolution equations

概 要 Miura transform is known as the transformation between Korteweg–de Vries (KdV) and modified

KdV (mKdV) equations. In this talk, based on the logarithmic representation of operators [1-9] in Banach
spaces, the mathematical structure of the Miura transform is explained in the detail. In conclusion, bymeans of the abstract version of the Miura transform [8] in Banach spaces, the representation of formal
solution to second order evolution equations is presented. It shows a rigorous-solution representation forboth infinitesimal generators and evolution operators (cf. the representation of exponentials in Hille–Yosida
theorem).
6 渡 辺 秀 司 (群 馬 大 理 工 )Shuji Watanabe (Gunma Univ.)

超伝導の BCS-Bogoliubov モデルにおける超伝導体の比熱の作用素論的研究 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

An operator-theoretical treatment of the specific heat of a superconductor in the BCS-Bogoliubov model of superconductivity

概 要 In the preceding talk, the present author gave a proof of the statement that the transition to asuperconducting state is a second-order phase transition in the BCS-Bogoliubov model of superconductivity
on the basis of fixed-point theorems, and solved the long-standing problem of the second-order phasetransition from the viewpoint of operator theory. In this talk we study the temperature dependence of thespecific heat of a superconductor in the model from the viewpoint of operator theory. We give the exact
and explicit expression for the gap in the specific heat divided by the specific heat. We then show that it
does not depend on superconductors and is a universal constant.
14:15〜15:15

2019 年度 (第 18 回) 日本数学会解析学賞受賞特別講演
廣 島 文 生 (九 大 数 理) 汎関数積分によるくりこみ理論と基底状態の非摂動的解析について

Fumio Hiroshima (Kyushu Univ.)

Renormalization and the ground state by functional integrations

概 要 The Nelson model is a typical quantum field model coupled with a Schrödinger operator. In orderto define this model as a self-adjoint operator, we first need UV cutoﬀ. Nelson himself proved that themodel can be renormalized about 50 years ago. Alternative proof using path integral was recently given by
Gubinell–Hiroshima–Lorinczi (14). Let H be the renormalized Nelson Hamiltonian. Although the explicit
form of H is unknown, Nelson himself gave H in a quadratic form. The existence of the ground state isshown by Hirokawa–Hiroshima–Spohn (05) when the coupling constant is suﬃciently small. The research on
the ground state of H has made great progress and final conclusions have been obtained in Hiroshima–Matte(19). We discuss the existence and absence of the ground state for arbitrary values of coupling constants by
Feynman–Kac formula, and the localization of the ground state is shown by using an infinite volume Gibbs
measure.
15:30〜16:30

特別講演
中 野 史 彦 (東 北 大 理) ♭ 1 次元ランダムシュレーディンガー作用素の固有値・固有関数のスケーリ
ング極限について()
Fumihiko Nakano Tohoku Univ.
Scaling limit of the eigenvalues and eigenfunctions of 1-dimensional ran-dom Schrödinger operators
概 要 One-dimensional Schrödinger operators have rich spectral and statistical properties, depending on the

decay order of the potential at infinity. In this talk, we discuss: (i) fluctuation of integrated density ofstates (ii) spectral statistics (iii) scaling limit of eigenfunctions

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函数解析学

56

9 月 23 日（水）10:30〜11:45
7 川 村 晃 英 (京大国際高等教育院) ♭ 球表現の分解と多変数超幾何型多項式の加法定理 · · · · · · · · · · · · · · · · · · · 15
Koei Kawamura (Kyoto Univ.)

Decomposition of spherical representations and an addition theorem for
multivariate hypergeometic polynomials

概 要 We aim addition theorems for multivariate Krawtchouk polynomials, following Dunkl [2] for 1-variatecase. We work on harmonic analysis on a nonArchimedean local field, that is a group theoretic situation
where these polynomials play roles of the zonal spherical functions. We need some hypotheses to make thefunctions decomposed with multiplicity free. Then we have an addition theorem for multivariate Krawtchouk
polynomials which includes expansions by multivariate Hahn polynomials.
8 中 島 秀 斗 (名 大 多 元 数 理)

Hideto Nakashima (Nagoya Univ.)

一般化 Vinberg 錐上の不変微分作用素環における Capelli 型恒等式について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On Capelli-type identities of rings of invariant diﬀerential operators on
generalized Vinberg cones

概 要 We consider rings of diﬀerential operators on generalized Vinberg cones, which are invariant under

the actions of split solvable Lie groups acting on the cones simply transitively. Explicit expressions of theirgenerators are given. Moreover, we present Capelli-type identities for these cones.
9 示 野 信 一 (関西学院大理工)谷
直 哉 (関西学院大理工)Nobukazu Shimeno(Kwansei Gakuin Univ.)
Naoya Tani (Kwansei Gakuin Univ.)

Dunkl 解析における Pizzetti の公式の拡張 · · · · · · · · · · · · · · · · · · · · · · · · · 15
An extension of Pizzetti’s formula in Dunkl analysis

概 要 We give an extension of Pizzetti’s formula associated with the Dunkl operators. It gives an explicit

formula for the Dunkl inner product of an arbitrary function and a homogeneous Dunkl harmonic polynomial
on the unit sphere.
10 示 野 信 一 (関西学院大理工)
本 田 龍 央織 田寛 (拓 殖 大 工)
Nobukazu Shimeno(Kwansei Gakuin Univ.)
Tatsuo Honda
Hiroshi Oda (Takushoku Univ.)

Hypergeometric Fourier transform associated with a root system of type
BC · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Hypergeometric Fourier transform associated with a root system of typeBC

概 要 We give the inversion formula and the Plancherel formula for the hypergeometric Fourier transform

associated with a root system of type BC, when the multiplicity parameters are not necessarily nonnegative.

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57

函数解析学

13:15〜14:15

特別講演
中 濱 良 祐 (九 大 I M I )Ryosuke Nakahama (Kyushu Univ.)

正則離散系列表現の制限に関する絡作用素の構成

Construction of intertwining operators for restriction of holomorphic
discrete series representations

概 要 Let G be a Lie group, G′ ⊂ G be a closed subgroup, and we consider a unitary representation H of

G. Then in general, the restriction H|G′ decomposes into a direct integral of irreducible representations of
G′ . Especially, if H is in a nice class of representations called “holomorphic discrete series representations”
and (G, G′ ) is a “symmetric pair of holomorphic type”, then H|G′ decomposes discretely, and there exist
G′ -intertwining operators between H|G′ and a representation H′ of the subgroup G′ of both directions. The
projection operator H|G′ → H′ (the symmetry breaking operator) is always given by a diﬀerential operator,
and the embedding operator H′ → H|G′ (the holographic operator) is given by an infinite-order diﬀerential
operator. In this talk the speaker gives the results on explicit construction of these intertwining operators
when (G, G′ ) = (Sp(n, R), U (p, q)).

9 月 24 日（木）10:00〜12:00
同大)
11 田 中 清 喜 (大山 路 哲 史 (神 戸 工 高 専 )Kiyoki Tanaka (Daido Univ.)
Satoshi Yamaji(Kobe City Coll. of Tech.)

Bergman 空間上の little Hankel 作用素の本質ノルムの評価について · · 15
Essential norm estimates for little Hankel operators on Bergman spaces

概 要 Bonami–Luo gave a characterizaion of bounded little Hankel operators on Bergman spaces with anti

holomorphic symbols. In this talk, we announce a result of essential norm estimates for little Hankel
operators on Bergman spaces with anti holomorphic symbols. In particular, we give a characterization ofcompactness of little Hankel operators on Bergman spaces with anti holomorphic symbols.
12 飯 田 安 保 (金 沢 医 大)Yasuo Iida (Kanazawa Med. Univ.)

Zygmund F -algebra の有界部分集合について · · · · · · · · · · · · · · · · · · · · · · 15
Bounded subsets of the Zygmund F -algebra

概 要 We will consider some characterizations of boundedness in the Zygmund F -algebra N logα N (X) (α >0) of holomorphic functions f on the unit polydisk or the unit ball that satisfy∫
supφα (log+ |f (rζ)|) dσ(ζ) < ∞,
0≤r<1

∂X

where φα (t) = t{log(cα + t)}α for t ≥ 0 and cα = max{e , eα }.
13 植 木 誠 一 郎 (東 海 大 理)
Sei-Ichiro Ueki

(Tokai Univ.)

Isometries of the Novinger–Oberlin type Privalov space · · · · · · · · · · · · · 10
Isometries of the Novinger–Oberlin type Privalov space

概 要 We introduce the space of analytic functions on the open unit disk whose derivative belong to thePrivalov space. We will give the characterization of a linear isometry of this space. We also characterize
the surjective, not necessarily linear, multiplicative isometry of this space.

最終版: 2020/08/22
函数解析学

14 大 井 志 穂 (新 潟 大 理)
Shiho Oi

(Niigata Univ.)58

行列環に値をとる Lipschitz 環の間の全射等距離写像について · · · · · · · · 15

Surjective linear isometries on algebras of Lipschitz maps with the values
in the matrix algebra

概 要 The study of isometries on vector-valued Lipschitz maps with the ℓ1 -norm has been researched recently.

To develop the study, we show Hermitian operators on spaces of Lipschitz maps taking values in finite
dimensional Banach spaces are composition operators. By the characterization, we give a characterization
for unital surjective linear isometries on spaces of Lipschitz maps with the values in the algebra of complex
matrices.
大薬)
15 丹 羽 典 朗 (日三 浦
毅 (新 潟 大 理)

(Nihon Univ.)
Norio Niwa
Takeshi Miura (Niigata Univ.)

正則関数からなる Banach 空間上の全射等距離写像について, II · · · · · · · 15

Surjective isometries on a Banach space of analytic functions on the
open unit disc, II

概 要 In this talk, we will consider the forms of surjective isometries on some Banach space of analytic

functions on the open unit disc.
16 三 浦毅 (新 潟 大 理)

Takeshi Miura (Niigata Univ.)

正則関数のなすリプシッツ空間上の全射等距離写像 · · · · · · · · · · · · · · · · · 15

On surjective isometries on Lipschitz space of analytic functions

概 要 We characterize surjective, not necessarily linear, isometries on Lipschitz space of all analytic functions

on the open unit disc.
17 古 清 水 大 直 (米 子 工 高 専)
三 浦
毅 (新 潟 大 理)
Hironao Koshimizu(Yonago Nat. Coll. of Tech.)Takeshi Miura (Niigata Univ.)

関数環に値をとる C 1 空間とその上の全射等距離写像 · · · · · · · · · · · · · · · · 15

Surjective isometries on uniform algebra valued C 1 space

概 要 Let A be a uniform algebra. We denote by C 1 ([0, 1], A) the complex linear space of all A-valued

continuously diﬀerentiable maps on the closed unit interval [0, 1]. We give the characterization of surjective,
not necessarily linear, isometries on C 1 ([0, 1], A).
14:15〜15:10
18 濱 田 裕 康 (佐 世 保 工 高 専)
Hiroyasu Hamada(Sasebo Nat. Coll. of Tech.)C∗ -algebras generated by multiplication operators and composition operators by functions with self-similar branches · · · · · · · · · · · · · · · · · · · · · 15C∗ -algebras generated by multiplication operators and composition operators by functions with self-similar branches

概 要 Let K be a compact metric space and let φ : K → K be continuous. We study C∗ -algebra MC φgenerated by all multiplication operators by continuous functions on K and a composition operator Cφ
induced by φ on a certain L2 space. Let γ = (γ1 , ..., γn ) be a system of proper contractions on K. Supposethat γ1 , ..., γn are inverse branches of φ and K is self-similar. We consider the Hutchinson measure µH of
γ and the L2 space L2 (K, µH ). Then we show that the C∗ -algebra MC φ is isomorphic to the C∗ -algebraOγ (K) associated with γ under some conditions.

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59

函数解析学

19 渚
勝 (千 葉 大 理 )大 坂 博 幸 (立 命 館 大 理 工 )P. Bag(Narsee Monjee Inst. of Management Stud.)S. Dey(Indian Inst. of Tech. Bombay)
Masaru Nagisa (Chiba Univ.)
Hiroyuki Osaka (Ritsumeikan Univ.)
Priyabrata Bag(Narsee Monjee Inst. of Management Stud.)Santanu Dey(Indian Inst. of Tech. Bombay)

Schmidt ランクと部分空間 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Subspaces generated by orthonormal vectors of some Scmidt ranks

概 要 We consider a bipartite Hilbert space H = Cm ⊗ Cn . When n, m ≥ 4, we construct three subspaces(S ⊃ T ⊃ U) of H. These subspaces are generated by orthonormal vectors which have a special Schmidt
rank. Our interst is to give a special form of bases for them.
20 瀬 尾 祐 貴 (大阪教育大教育)
Yuki Seo (Osaka Kyoiku Univ.)

多変数行列幾何平均に対するノルム不等式 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Norm inequalities of n-variable matrix geometric means

概 要 In this talk, we show norm inequalities of matrix power means, by using a Ando–Hiai type comple-

mentary inequality of matrix power means. As an application, we show norm inequalities of the Karcher
mean of positive definite matrices. These results are extensions of two-variable version with respect to thematrix geometric mean.
15:20〜16:20

特別講演
渡 邉 恵 一 (新 潟 大 理) ♭ メビウスジャイロベクトル空間とその間の連続写像のあるクラスについて

Keiichi Watanabe (Niigata Univ.)

On Möbius gyrovector spaces and a class of continuous mappings between them

概 要 We study some aspects of Möbius gyrovector spaces from viewpoints of basic theory of functional

analysis. First of all, I introduce the notion of gyrocommutative gyrogroups, gyrovector spaces and Möbius
gyrovector spaces due to A. A. Ungar. Then I present some fundamental results such as the structureof finitely generated gyrovector subspaces, orthogonal gyrodecomposition and gyroexpansion, Cauchy–
Bunyakovsky–Schwarz type inequalities, continuous quasi gyrolinear functionals and a class of continuous
mappings between Möbius gyrovector spaces corresponding Hilbert space operators.

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統計数学

統

計

数

60

学

9 月 22 日（火）9:00〜12:00
1 得 重 雄 毅 (京 大 数 理 研) ♭ ランダム木グラフ上のバイアス付き RW · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Yuki Tokushige (Kyoto Univ.)

Biased RWs on random trees

概 要 In this talk, we will discuss biased RWs on Galton–Watson trees, which are very classic model ofrandom trees. In particular, we aim at explaining intricate interplay between the bias to which a random
walk is subjected and a complicated geometric structure of Galton–Watson trees. This talk is based on
joint works with Adam Bowditch (National University of Singapore).
2 中 島 由 人 (京 大 人 間 環 境)
Yuto Nakajima (Kyoto Univ.)

シエルピンスキーガスケットの断面の次元について · · · · · · · · · · · · · · · · · 15

Dimensions of slices through the Sierpiński gasket

概 要 We discuss the intersections of the d-dimensional Sierpiński gasket with (d−1)-dimensional hyperplanes

in a particular fixed direction. We give the values of the Hausdorﬀ dimension, the lower box dimension,
the upper box dimension, and the packing dimension of each slice and determine the criterion for which theHausdorﬀ dimension of the slice takes Marstrand’s value.
3 大 坂 翔 人 (横 浜 国 大 理 工)
竹 居 正 登 (横 浜 国 大 工)

Shoto Osaka (Yokohama Nat. Univ.)
Masato Takei (Yokohama Nat. Univ.)

高木クラスの関数における収束の速さについて · · · · · · · · · · · · · · · · · · · · · 15

On the rate of convergence for Takagi class functions

概 要 We consider a generalized version of the Takagi function, which is one of the most famous example

of nowhere diﬀerentiable continuous functions. We investigate a set of conditions to describe the rate ofconvergence of Takagi class functions from the probabilistic point of view: The law of large numbers, thecentral limit theorem, and the law of the iterated logarithm. On the other hand, we show that the Takagi
function itself does not satisfy the law of large numbers in the usual sense.
4 イェーリッシュヨハネス
(名 大 多 元 数 理)
高 橋 博 樹 (慶 大 理 工)

Johannes Jaerisch (Nagoya Univ.)
Hiroki Takahasi (Keio Univ.)

Mixed Birkhoﬀ spectra of one-dimensional Markov maps · · · · · · · · · · · · 15

Mixed Birkhoﬀ spectra of one-dimensional Markov maps

概 要 For Markov maps of the interval with countably many branches and finitely many neutral periodic

points, we establish a conditional variational formula for the mixed multifractal spectrum of Birkhoﬀ averagesof countably many observables, in terms of the Hausdorﬀ dimension of invariant probability measures.
5 星 野 浄 生 (阪 府 大 理)

Kiyoiki Hoshino (Osaka Pref. Univ.)

On a Riemann approximation of the stochastic integral · · · · · · · · · · · · · 15
On a Riemann approximation of the stochastic integral

概 要 We introduce a Riemann-type sum regarded as generalizations of the sums which define the Nualart–

Pardoux–Stratonovich integral and the Ogawa integral with respect to the Haar system, and discuss theapproximation of some stochastic integrals by this sum. We attempt to characterize some stochastic
integrabilities by conditions on the Riemann sum, by which we also introduce a variation of the stochastic
k-integral and give an application example of this related to the volatility estimation.

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6 池 田 光 優 (阪 大 基 礎 工 )Mitsumasa Ikeda (Osaka Univ.)

A new discretization scheme for one dimensional stochastic diﬀerential
equations using time change method · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A new discretization scheme for one dimensional stochastic diﬀerential
equations using time change method

概 要 We propose a new numerical method for one dimensional stochastic diﬀerential equations (SDEs).

The main idea of this method is based on a representation of a weak solution of a SDE with a timechanged Brownian motion, dated back to Doeblin (1940). In cases where the diﬀusion coeﬃcient is boundedand β-Hölder continuous with 0 < β ≤ 1, we provide the rate of strong convergence. An advantage of
our approach is that we approximate the weak solution, which enables us to treat a SDE with no strong
solution. Our scheme is the first to achieve the strong convergence for the case 0 < β < 1/2.
7 濵 口 雄 史 (京大理)

Yushi Hamaguchi (Kyoto Univ.)

Time-inconsistent stochastic recursive control and backward stochastic
Volterra integral equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Time-inconsistent stochastic recursive control and backward stochastic
Volterra integral equations

概 要 In the recent years, time-inconsistent stochastic control problems have received remarkable attentions

in stochastic control, mathematical finance and economics. In this talk, we investigate a Nash equilibrium
control for a time-inconsistent stochastic recursive control problem where the cost functional is defined by
the solution to a backward stochastic Volterra integral equation (BSVIE, for short), which is a generalizationof a backward stochastic diﬀerential equation (BSDE, for short). We provide a necessary and suﬃcientcondition for a Nash equilibrium control via variational methods. The key point of our analysis is toderive the corresponding adjoint equations wihch turn out to be the so-called extended backward stochastic
Volterra integral equations (EBSVIEs, for short).
8 市 原 直 幸 (青 学 大 理 工 )Naoyuki Ichihara(Aoyama Gakuin Univ.)

内向き有界ドリフトを持つエルゴード型確率制御に現れる相転移について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Phase transitions arising in stochastic ergodic control with bounded
inward drift

概 要 We are concerned with certain phase transition phenomena arising in a family of stochastic ergodic

control problems having some real parameter. We assume that the drift vector of the controlled diﬀusion
is bounded and inward pointing and the potential function in the cost functional is positive and vanishingat infinity. Then, it may happen that the large time behavior of the optimal diﬀusion changes drasticallyin the vicinity of some critical value of the parameter. We specify a necessary and suﬃcient condition
so that such a phase transition occurs. The key lies in the analysis of solutions to the associated viscous
Hamilton–Jacobi equation of ergodic type.
9 古 城 克 也 (新 居 浜 工 高 専 )Katsuya Kojo
(Nat. Inst. of Tech., Niihama Coll.)

スペクトル測度が point mass だけで構成される多次元対称安定分布の決定性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On the determinism of multivariate symmetric stable distributions whose
spectral measures are constructed by point masses

概 要 When d ≥ 3, we study the existence of a diﬀerent d-dimensional symmetric stable distribution whichshares the same (d − 1)-dimensional marginal distributions with a given d-dimensional symmetric stable
distribution whose spectral measure is constructed by point masses.

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♭
安定過程とその最大の密度関数評価について · · · · · · · · · · · · · · · · · · · · · · · 15
10 J. González Cázares(Warwick Univ.・The Alan Turing Inst.)
Arturo Kohatsu Higa
(立 命 館 大 理 工)
A. Mijatović
(Warwick Univ.・The Alan Turing Inst.)

Jorge González Cázares(Warwick Univ./The Alan Turing Inst.)
Higa Aruturo Kohatsu(Ritsumeikan Univ.)
Aleksandar Mijatović
(Warwick Univ./The Alan Turing Inst.)

The density of a stable process and its maximum

概 要 We discuss integration by parts formulas for the joint law of a stable process and its maximum.

The argument is based on a multi-level representation for the joint law which uses the theory of convex
majorants for stable processes and the Chambers–Mallows–Stuck representation for stable random variables.
As applications, we obtain regularity results for the joint law and upper bounds for the density and its space
derivatives up to the boundary.
11 新 井 裕 太 (千葉大融合理工)
Yuta Arai(Chiba Univ.)

The KPZ fixed point for discrete time geometric TASEP · · · · · · · · · · · · 15
The KPZ fixed point for discrete time geometric TASEP

概 要 The totally asymmetric simple exclusion process (TASEP) is one of the prototypical interacting

stochastic particle systems and can be interpreted as a stochastic growth model of an interface, which turns
out to belong to the Kardar–Parisi–Zhang (KPZ) universality class. In this talk, we consider the discrete
time geometric TASEP with parallel update. In these processes, we get a single Fredholm determinant
representation for the joint distribution function of particle positions with arbitrary initial data. Using
this, for the discrete time geometric TASEP, we show that in the KPZ 1:2:3 scaling limit, the distributionfunction converges to the one describing the KPZ fixed point was introduced by Matetski, Quastel, andRemenik (2018).
12 河 備 浩 司 (慶 大 経 済) ♭ Uniqueness of Dirichlet forms related to stochastic quantization under
S. Albeverio ( Univ. of Bonn ) exponential/trigonometric interactions on the two-dimensional torus · · 15)
BaFin
S.-R. Mihalache (M. Röckner (Bielefeld Univ.)
Hiroshi Kawabi (Keio Univ.)
Sergio Albeverio (Univ. of Bonn)
Stefan-Radu Mihalache (BaFin)
Michael Röckner (Bielefeld Univ.)

Uniqueness of Dirichlet forms related to stochastic quantization under
exponential/trigonometric interactions on the two-dimensional torus

概 要 In this talk, we consider Dirichlet forms given by two-dimensional space-time quantum fields withexponential/trigonometric interactions in finite volume. In the context of Euclidean quantum field theory,the former quantum field and the latter one are called the Hoegh–Krohn model and the sine-Gordon model,
respectively. We prove strong uniqueness of the corresponding Dirichlet operator and construct a weaksolution (in the probability sense) of the modified-stochastic quantization equation under suitable conditions
on the charge constant and the regularization parameter.

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14:20〜15:20

特別講演
阿 部 圭 宏 (千 葉 大 理 )Yoshihiro Abe(Chiba Univ.)

ランダムウォークの被覆問題

Covering problems for random walks

概 要 The covering process by a simple random walk on a finite lattice has been intensively studied byphysicists and probabilists. They have been especially interested in the cover time, which is the first timeat which the walk visits every vertex and statistics of unvisited points, called late points. They have founddimension-dependent properties in the covering process. In three and higher dimensions, late points are
independent and uniform in some sense and the cover time converges in law to a Gumbel distribution. In
two dimensions, late points are fractal-like and forms clusters and it is believed that the cover time would
weakly converge to a randomly-shifted Gumbel distribution. In this talk, I will review research on thesecovering problems.
15:40〜16:40

特別講演
香 取 眞 理 (中 大 理 工 )Makoto Katori(Chuo Univ.)

行列式点過程の楕円関数拡張

Elliptic extensions of determinantal point processes

概 要 A point process is a statistical ensemble of random nonnegative-integer-valued Radon measures ona space equipped with a reference measure. We consider the case in which for any integer n an n-point
correlation function is well defined with respect to the n-product of reference measure. When an n-point
correlation function is given by a determinant of n × n matrix for every n and the entries of matrices
are determined by a kernel of an integral operator, the point process is said to be determinantal andthe kernel is called the correlation kernel. Many examples of determinantal point processes (DPPs) havebeen studied in random matrix theory and correlation kernels provide reproducing kernels which construct
reproducing kernel Hilbert spaces. Recently we are interested in the DPPs in which correlation kernels
are expressed using Jacobi’s theta functions and Weierstrass’ elliptic functions. In the present talk wewill explain that these new examples of DPPs can be regarded as elliptic extensions of the classical DPPs
and their q-extensions (trigonometric extensions). In particular we will report an elliptic extension of thebeautiful work by Peres and Virág published in 2005, who considered the Gaussian analytic function (GAF)
on a unit disk D defined as an ensemble of random power series with i.i.d. complex Gaussian coeﬃcients.
There the covariance kernel of GAF is given by the reproducing kernel of the Hardy space on D called theSzegő kernel of D. They showed that zeros of the GAF form a DPP whose correlation kernel is equal to the
Bergman kernel of D. This talk is based on the joint work with Tomoyuki Shirai (IMI, Kyushu University).

9 月 23 日（水）9:00〜11:15
13 藤 田 敏 治 (九 工 大 工)
Toshiharu Fujita(Kyushu Inst. of Tech.)

合流型推移をもつマルコフ決定過程における政策について · · · · · · · · · · · 10

On policy for Markov decision process with converging branch system

概 要 We consider a Markov decision process model with a converging branch system which is one of

the nonserial transition systems. We have introduced recursive equations by using dynamic programming
technique. In this study, we investigate the optimal policy obtained by our recursive equations.

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統計数学

14 地 嵜 頌 子 (大 阪 工 大 情 報)宮 本 暢 子 (東 京 理 大 理 工)波大⋆)藤 原 良 叔 (筑Shoko Chisaki (Osaka Inst. of Tech.)
Nobuko Miyamoto (Tokyo Univ. of Sci.)
Ryoh Fuji-Hara (Univ. of Tsukuba⋆)

64

Uniform dropout designs with applications · · · · · · · · · · · · · · · · · · · · · · · · 15

Uniform dropout designs with applications

概 要 Dropout is used in deep learning. It is a method of learning by invalidating nodes with randomly foreach layer in the multi-layer neural network. And it deletes a random sample of activations (nodes) to zero
during the training process. A random sample of nodes cause more irregular frequency of dropout edges.
A dropout design is a combinatorial design on dropout nodes from each partite which balances frequency ofedges. In this talk, we give some related structure and properties with dropout designs.
15 盧
暁 南 (山 梨 大 工)
三 嶋 美 和 子 (岐 阜 大 工)
宮 本 暢 子 (東 京 理 大 理 工)
神 保 雅 一 (中部大現代教育)

Xiao-Nan Lu (Univ. of Yamanashi)
Miwako Mishima (Gifu Univ.)
Nobuko Miyamoto (Tokyo Univ. of Sci.)
Masakazu Jimbo (Chubu Univ.)

Circulant almost orthogonal arrays and perfect binary sequences · · · · · 15

Circulant almost orthogonal arrays and perfect binary sequences

概 要 Circulant almost orthogonal arrays (CAOAs) are a class of circulant arrays introduced by Y.-L. Lin,F. K. H. Phoa, and M.-H. Kao [Ann. Stat., 45(6), 2483–2510, 2017] as designs for fMRI experiments. In thistalk, I will focus on k × n two-level CAOAs with strength 2 and bandwidth 1, denoted by CAOA(n, k, 2, 2, 1),
and talk about their optimality and the D-eﬃciency. Moreover, by showing the relationship between
CAOA(n, k, 2, 2, 1) and perfect balanced binary sequences which are well studied in information theory, new
CAOA(n, k, 2, 2, 1) with large k and high D-eﬃciency are obtained.
16 松 原 和 樹 (中 央 学 院 大 商)島
大⋆)景 山 三 平 (広Kazuki Matsubara(Chuo Gakuin Univ.)
Sanpei Kageyama (Hiroshima Univ.⋆)

The existence of perpendicular multi-arrays · · · · · · · · · · · · · · · · · · · · · · · 15
The existence of perpendicular multi-arrays

概 要 Li et al. have newly introduced a combinatorial array, called a perpendicular multi-array, in 2018 forconstructions of splitting authentication codes having some perfect t-fold secrecy. In this talk, necessary
conditions for the existence of a perpendicular multi-array are discussed, and it is shown that the necessary
conditions are also suﬃcient for the existence of a perpendicular multi-array with block size 3 × 2 withthe only one exception. Finally, the asymptotic existence of perpendicular multi-arrays with a cyclic
automorphism is presented.
17 四 丸 直 人 (岡 山 理 大 理)
永 吉 峻 章 (岡 山 理 大 理)
佐 藤 宏 樹 (岡 山 理 大 理)

Naoto Shimaru (Okayama Univ. of Sci.)
Toshifumi Nagayoshi(Okayama Univ. of Sci.)
Hiroki Sato (Okayama Univ. of Sci.)

On the χ2 statistics of leading digits of irrational rotations with a large
first or second partial quotient · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On the χ2 statistics of leading digits of irrational rotations with a large
first or second partial quotient

概 要 We derive exact formulas for the χ2 statistics of the distribution of the leading digit of an , where

log10 a has a large first or second partial quotient in its continued fraction expansion.

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18 米 永 航 志 朗 (北 大 経 済)
鈴 川 晶 夫 (北 大 経 済 )Koshiro Yonenaga (Hokkaido Univ.)
Akio Suzukawa (Hokkaido Univ.)

On exact distributions of the linear discriminant function in a Bayesiansetting · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On exact distributions of the linear discriminant function in a Bayesiansetting

概 要 Sampling distributions for the linear discriminant function are very complicated and they are noteasily calculated. As a result, the great attention has been paid to derive asymptotic expansions for the
linear discriminant function. However, asymptotic expansions cannot be expected to approximate the exact
distributions of the linear discriminant function for small sample sizes. In this report, we consider the
distributions of the linear discriminant function in a Bayesian setting. We derive the predictive density forthe linear discriminant function. This density are expressed as one dimensional integral. In addition, it isapplied to derive the cumulant generating function and cumulative distribution functions.
19 八 木 文 香 (東 京 理 大 理)
小 野 沢 瑞 季 (文京区立昭和小)
瀬 尾
隆 (東 京 理 大 理 )Ayaka Yagi (Tokyo Univ. of Sci.)
Mizuki Onozawa(Showa Elementary School)
Takashi Seo (Tokyo Univ. of Sci.)

2 標本問題における 2-step 単調欠測データの下での平均ベクトルに対する新たな検定統計量 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A new test statistic for two mean vectors with two-step monotone missing data

概 要 Testing problem for the equality of two mean vectors with two-step monotone missing data is

considered. Yu et al. (2006) proposed the T 2 -type test statistic for this problem and gave the approximation
to the upper percentiles of this statistic. Yagi et al. (2018) derived its approximate null distribution in theform of an asymptotic expansion. In this talk, we propose a new test statistic which replaced part of theabove statistic. Further, we exactly derive an asymptotic expansion for the new test statistic. Moreover, we
present the approximation to the upper percentiles of this statistic based on Yu et al. (2006) and propose
the transformed test statistics. Finally, we numerically investigate the accuracy and asymptotic behaviorof the proposed approximation and transformed test statistics.
20 柿 沢 佳 秀 (北 大 経 済)

Yoshihide Kakizawa (Hokkaido Univ.)

多変量バーンバウムサンダース型分布と密度推定への応用 · · · · · · · · · · · 15

Multivariate BS type distribution and its application to nonparametricdensity estimation

概 要 In this talk, we consider nonparametric density estimation for the data supported on [0, ∞)d . To define

a new estimator, we first review the Birnbaum–Saunders (BS) distribution theory, together with various
extensions (non-central version, elliptical-based construction, link to its logarithm version, and skew-based
construction). Then, we study the asymptotic properties of the proposed density estimator in the bivariatecase.
21 五 十 嵐 岳 (筑波大システム情報)

Gaku Igarashi (Univ. of Tsukuba)

ノンパラメトリックベータカーネル密度比推定による確率密度の不連続性検定 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A test on discontinuity of densities using nonparametric beta kernel
density ratio estimation

概 要 The kernel density estimation requires an assumption of continuity (smoothness) of an estimateddensity. Even if the underlying density has some discontinuity points, the features are not estimated. In
this talk, a test on discontinuity of a density is discussed. The nonparametric beta kernel direct density
ratio estimator proposed by Igarashi (2020) is applied to obtain a test statistic.

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統計数学

11:30〜12:00

66

統計数学分科会総会

9 月 24 日（木）9:00〜11:50
22 後 藤 佑 一 (早 大 理 工)
Yuichi Goto

(Waseda Univ.)

Distribution free tests for structural break of counting processes · · · · · 15
Distribution free tests for structural break of counting processes

概 要 In this talk, we discuss testing for a structural break of counting processes. Intensity functions of thecounting processes in our models have non-linear dependence structures including INGARCH(p,q) models.
We elucidate the asymptotic null distributions of the Wald, modified Wald, score, residual based CUSUM
test statistics, and these enable us to construct distribution-free tests. Moreover, the test based on themodified Wald statistic is consistent in the sense of power. A simulation suggests that the residual based
test is best among the proposed tests.
23 Yujie Xue(早 大 理 工)

The pros of cons on the combination of linear quantile regression and
LASSO with long-memory disturbances · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Yujie Xue

(Waseda Univ.)

The pros of cons on the combination of linear quantile regression and
LASSO with long-memory disturbances

概 要 In this talk, LASSO is applied to the linear quantile regression models with long-memory disturbances.

Considering that there exists the situation that the norm of diﬀerent column in the regression matrix may
have diﬀerent order of sequence length n, we introduce a modified LASSO estimator where the tuning
parameter λ is not a scalar but a vector. Two situations where the dimension of parameters p is fixed,
and where p increases as n increases are discussed. Besides, some simulation studies are examined with acomparison with some other approaches.
24 劉
言 (早 大 理 工)
木 村 晃 敏 (早 大 理 工)
谷 口 正 信 (早 大 理 工)
H. Ombao(King Abdullah Univ. of Sci. Tech.)(Waseda Univ.)
Yan Liu
Akitoshi Kimura (Waseda Univ.)
Masanobu Taniguchi (Waseda Univ.)
Hernando Ombao(King Abdullah Univ. of Sci. Tech.)Topological analysis for local Granger causality · · · · · · · · · · · · · · · · · · · · 15

Topological analysis for local Granger causality

概 要 We propose a topological approach to statistically visualizing the Granger causality. Granger intro-

duced his celebrated new measure for the causality between multiple time series by prediction errors 50
years ago. We localize an alternative version of his idea, a natural refinement by Hosoya, and construct a
new theory based on locally stationary processes. Some causality relations between Japanese and US stocks
are wonderfully illustrated by our new methodology.

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25 明 石 郁 哉 (東 大 経 済)(Ruhr-Univ. Bochum)
H. Dette

Fumiya Akashi (Univ. of Tokyo)
Holger Dette (Ruhr-Univ. Bochum)

Robust regression on hyper-spheres with unspecified heteroscedastic errors · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Robust regression on hyper-spheres with unspecified heteroscedastic errors

概 要 Statistical treatment for a random vector on a hyper-spheres attracts a lot attention recently, andhas various applications such as seismic wave analysis, analysis for orientation of wild fire, etc. In thistalk the nonlinear regression model whose predictor is a random vector on a hyper-sphere is considered. It
is well known that the classical method in “linear statistic” does not work for spherical random vectors.
To construct a robust estimator for the nonlinear regression function, this talk employees L1-regression
method and kernel-type objective function. The proposed local-linear estimator has asymptotic normality
even if the error process has infinite variance, dependent structure or heteroscedasticity. Some simulation
experiments illustrate desired finite sample properties of the proposed method.
26 明 石 郁 哉 (東 大 経 済)
蛭 川 潤 一 (新 潟 大 理 )K. Fokianos (Lancaster Univ.)

Fumiya Akashi (Univ. of Tokyo)
Junichi Hirukawa (Niigata Univ.)
Konstantinos Fokianos(Lancaster Univ.)

Inference for heavy-tailed time varying processes by self-weighting · · · · 15

Inference for heavy-tailed time varying processes by self-weighting

概 要 This talk considers a parameter estimation problem of time-varying autoregressive models under thepresence of infinite variance. Although there is rich literature on locally stationary processes, the classicalpapers always assume the finite variance of the model. This talk constructs a robust estimator based on the
self-weighting approach proposed by Ling (2005, Journal of Royal Statistical Society B) and least absolutedeviations regression. The proposed estimator is show to be asymptotically normal regardless of whether
the error term has infinite variance or not. Finite sample performance of the proposed method is also
investigated by simulation experiments.
27 フスナキラティアティナ
(東 北 大 理 )赤 間 陽 二 (東 北 大 理 )Atina Husnaqilati (Tohoku Univ.)
Yohji Akama (Tohoku Univ.)

Component retention to microarray datasets and Marčhenko–Pastur
setting · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Component retention to microarray datasets and Marčhenko–Pastur
setting

概 要 By classical stopping rules Guttman–Kaiser rule, Jolliﬀe’s rule and a stopping rule based on broken-

stick model, we compute the number (ratio) of principal components to retain for microarray datasets, andfor Marčhenko–Pastur’s setting, i.e. the standard normal p-dimensional population with the sample size
n → ∞ being c = p/n fixed. For typical cDNA datasets, we have c > 10 and (Guttman–Kaiser) > (Broken
stick model) > (Jolliﬀe). For Marčhenko–Pastur setting, (Guttman–Kaiser) > (Jolliﬀe) for 0.4 < c < 2.5,
and broken stick model convergences to 0 for all c > 0.

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統計数学

28 佃
康 司 (九 大 数 理)
松 浦
峻 (慶 大 理 工)
Koji Tsukuda (Kyushu Univ.)
Shun Matsuura (Keio Univ.)

68

四つのウィシャート行列の積のトレースに関する高次元極限定理とその応用 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

High-dimensional limit theorem associated with trace of four Wishart
matrices and its application

概 要 The Wishart distribution is a classical distribution of random matrices, and a lot of studies haveinvestigated its asymptotic properties under the traditional regime of multivariate statistics: n → ∞ with
fixed p, where n denotes the degree-of-freedom and p is the size of the matrix parameter of the distribution.
On the other hand, recently more and more studies considered another regime of high-dimensional statistics:
n → ∞ together with p → ∞. In this presentation, we derive a new property of the Wishart distribution;in particular, the asymptotic normality of the trace of products of four independent Wishart matrices undera high-dimensional regime is shown. As an application of the result, we propose a test procedure for thecommon principal components hypothesis.
29 石 井晶 (東 京 理 大 理 工)
矢 田 和 善 (筑波大数理物質)
青 嶋
誠 (筑波大数理物質)
Aki Ishii (Tokyo Univ. of Sci.)
Kazuyoshi Yata (Univ. of Tsukuba)
Makoto Aoshima (Univ. of Tsukuba)

高次元固有ベクトルの検定について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A test procedure for high-dimensional eigenvectors

概 要 In this talk, we consider testing high-dimensional eigenvectors. We produce a test statistic by using

the extended cross-data-matrix (ECDM) methodology and show the unbiasedness of the ECDM test statistic
even in a high-dimensional setting. We also show that the test statistic holds the asymptotic normality.
We propose a new test procedure by using the asymptotic normality and evaluate its size and power
asymptotically. We also give a real data analysis by using a microarray data set.
30 中 山 優 吾 (京 大 情 報)
矢 田 和 善 (筑波大数理物質)
青 嶋
誠 (筑波大数理物質)
Yugo Nakayama (Kyoto Univ.)
Kazuyoshi Yata (Univ. of Tsukuba)
Makoto Aoshima (Univ. of Tsukuba)

Clustering by kernel principal component analysis for high-dimensional
data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Clustering by kernel principal component analysis for high-dimensionaldata

概 要 In this talk, we consider clustering based on the kernel principal component analysis (KPCA) for

high-dimensional data. We investigate asymptotic properties of the KPCA with the typical kernel functions
such as the linear kernel and the Gaussian kernel. We give theoretical reasons why the Gaussian kernel
is eﬀective for clustering high-dimensional data. In addition, we discuss a choice of the scale parameteryielding a high performance of the KPCA with the Gaussian kernel. We give asymptotic properties of the
KPCA in a general framework of the kernel functions. Finally, we check the performance of the clusteringby using numerical simulations and microarray data sets.

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69

統計数学

31 野 村昇 (高 知 大 理 工 )Noboru Nomura (Kochi Univ.)

象限確率計算におけるパラメータによる微分係数の評価 · · · · · · · · · · · · · 15

Evaluation of derivatives in the calculation of orthant probabilities withorthogonal projection

概 要 In this talk, a procedure to evaluate derivatives by parameters of orthant probabilities with Gaussian

distribution is considered. It is constructed by improving the procedure to evaluate the value of orthantprobabilities. The evaluation of an orthant probability is converted to a problem that random vector falls
in a polyhedral cone. The cone is divided into small cones and the probability that the vector falls in asmall cone is evaluated by a problem of smaller dimension and one-dimensional integral. For more than two
dimensional cases, the orthant probability is p-dimensional integral of probability density function, and its
derivative is the (p − 1)-dimensional integral. It is shown that the intermediate values required to evaluationthese integrals are shared in the procedure, and the derivatives of orthant probabilities can be given with asmall additional computational cost.
14:20〜15:20

特別講演
小 池 祐 太 (東 大 数 理 )Yuta Koike(Univ. of Tokyo)

高次元中心極限定理の最近の展開

Recent progress in high-dimensional central limit theorems

概 要 We review the recent progress of Gaussian approximation theory in high-dimensions. We obtaindiﬀerent approximation rates depending on how to quantify the distance between objective statistics andapproximating Gaussian vectors. We will also discuss the optimality of the existing approximation rates
and unsolved problems in this area.
15:40〜16:40
藤 森

特別講演
洸 (信 州 大 経 法 )Kou Fujimori (Shinshu Univ.)

高次元・スパースな設定における確率過程の統計モデルに対する Dantzig
selector
The Dantzig selector for statistical models of stochastic processes inhigh-dimensional and sparse settings

概 要 The Dantzig selector, which was proposed by Candés and Tao in 2007, is an estimation procedure

for regression models in high-dimensional and sparse settings. In this talk, the Dantzig selectors for somestatistical models of stochastic processes are discussed. We apply this procedure to Cox’s proportional
hazards model and some specific models of diﬀusion processes and prove the consistency and the variableselection consistencies of the estimators. Based on partial likelihood and quasi-likelihood methods whichwere studied intensively in low-dimensional settings, we study these statistical models of stochastic processes
in high-dimensional and sparse settings, which need some mathematically challenging tasks. The consistencyof the estimators are proved by using stochastic maximal inequalities which are derived from Bernstein’s
inequalities for martingales and conditions on Hessian matrices of likelihood which are known as the restricted
eigenvalue conditions. We prove that consistency of the estimator implies the variable selection consistency
which enables us to reduce the dimension. Using the dimension reduction, asymptotically normal estimators
can be constructed.

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応用数学

応

用

数

70

学

9 月 22 日（火）9:50〜11:45
1 釣 井 達 也 (大阪人間科学大人間)
伊 藤 直 治 (奈良教育大教育)
松 山 豊 樹 (奈良教育大教育)
Tatsuya Tsurii(Osaka Univ. of Human Sci.)
Naoharu Ito (Nara Univ. of Edu.)
Toyoki Matsuyama(Nara Univ. of Edu.)

頂点数 n のループ付き完全グラフ上の n 状態 Fourier walk の周期性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Periodicity of n-state Fourier walks on complete graphs with self-loops

概 要 This paper studies n-state Fourier walks on complete graphs with a self-loop at each vertex. The

periodicity of the n-state Fourier walk has been determined by its evolution matrix. It is shown that then-state Fourier walk is periodic with period 4n.
2 石 川 彩 香 (横 浜 国 大 理 工)

Ayaka Ishikawa (Yokohama Nat. Univ.)

グラフ上に定まる量子ウォークモデルの族 · · · · · · · · · · · · · · · · · · · · · · · · · 15

A family of quantum walks on finite graphs

概 要 The Grover walk is a quantum walk model on a finite graph. Konno–Sato’s theorem implies that theGrover transition matrix is the edge matrix of the weighted zeta functions of the 2nd kind. The weighted
zeta function of the 2nd kind belongs to a wider class of graph zeta functions, called the generalized weighted
zeta functions. We give a family of quantum walk models corresponding to the generalized weighted zetafunctions, which contains the Grover walk.
3 松 江
要 (九 大 I M I)
瀬 川 悦 生 (横浜国大環境情報)

Kaname Matsue (Kyushu Univ.)
Etsuo Segawa (Yokohama Nat. Univ.)

ユニタリ量子ウォークと開放系量子ウォークの補間 · · · · · · · · · · · · · · · · · 15

An interpolation between unitary quantum walk and open quantum
random walk

概 要 We introduce an intermediate walk between unitary quantum walks and open quantum random

walks on one-dimensional lattice by controlling decoherence with parameters s ≤ 0 ≤ t. If s = t = 0
and s = −∞, t = ∞, then an open quantum random walk and a unitary quantum walk are recovered,respectively. The fundamental idea is based on considering a quantum walk with the Dirichlet cut of the
stripe Ds,t ⊂ {(x, y) ∈ Z | s ≤ x − y ≤ t} in the two-dimensional lattice and introducing a measure on the
diagonal line x = y. We demonstrate that the width of the stripe controls the strength of the decoherence
by a numerical simulation and also analytically show spectral analysis and limit theorems on the case for|s − t| = 1 using Kato’s perturbation theory.
4 佐
今
三
森

藤
巖 (小 山 工 高 専)
野 紀 雄 (横 浜 国 大 工)
橋 秀 生 (法 政 大 理 工)
田 英 章 (室 蘭 工 大 工)

Iwao Sato (Oyama Nat. Coll. of Tech.)
Norio Konno (Yokohama Nat. Univ.)
Hideo Mitsuhashi (Hosei Univ.)
Hideaki Morita (Muroran Inst. of Tech.)

The trace formula with respect to the Grover matrix of a graph · · · · · · 15

The trace formula with respect to the Grover matrix of a graph概 要 We present a trace formula with respect to the Grover matrix that is the transition matrix of theGrover walk on a graph.

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71

応用数学

5 森 田 英 章 (室 蘭 工 大 工 )Hideaki Morita (Muroran Inst. of Tech.)

行列式表示をもたないグラフゼータについて · · · · · · · · · · · · · · · · · · · · · · · 15

On the Hashimoto expression for graph zeta functions

概 要 It is observed that graph zeta functions usually have the determinant expression of Hashimoto type.

In this talk, we will see that there are a graph zeta which does not have the Hashimoto expression and it
arises naturally in the usual context of graph zetas.
6 小 林 雅 人 (神 奈 川 大 工) ♭ q-determinant, q-Vandermonde and signed bigrassmannian polynomials· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Masato Kobayashi (Kanagawa Univ.)

q-determinant, q-Vandermonde and signed bigrassmannian polynomials

概 要 In combinatorics, it is always interesting to ask what a q-analog of something is. In studying theposet structure of alternating sign matrices around 2015, I came up with a series of three ideas as in thetitle. In particular, the first two are more general ideas of the classical determinant and Vandermonde. In
my talk, I will give more details.
7 沼 田 泰 英 (信 州 大 理 )矢 澤 明 喜 子 (信州大総合医理工)Yasuhide Numata (Shinshu Univ.)
Akiko Yazawa (Shinshu Univ.)

ループ付き完全グラフから決まる行列の固有値について · · · · · · · · · · · · · 15

The eigenvalues of a matrix defined by the complete graph with selfloops

概 要 We consider a matrix whose indices are the edge of the complete graph with selfloops. Assume that

entries are the same if the indices are isomorphic as graphs. We compute the eigenvalues of this matrix.
We also apply the main theorem to the eigenvalues of the second Hessian matrix with respect to divided
power operators of the elementary symmetric polynomial el (xk1 , . . . , xkn ).
14:15〜15:30
8 八 森 正 泰 (筑波大システム情報)
Masahiro Hachimori(Univ. of Tsukuba)

Nonpure な単体的複体と順次分割可能性 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Nonpure simplicial complexes and sequential partitionability

概 要 In this talk we consider three kinds of stronger variations of partitionability of nonpure simplicial

complexes: (A) having a partition in a sequential manner, (B) having a partition compatible with its
h-triangle, (C) the simplicial complex itself as well as its every pure skeletons are partitionable. We showthat (A) and (B) are equivalent, and that (C) is strictly weaker than the others. We call this (A) and (B)as sequential partitionability. As examples of such sequentially partitionable simplicial complexes, we thenshow that simplicial complexes with star-shaped realizations are sequentially partitionable.
9 宮 崎 充 弘 (京 都 教 育 大 )Mitsuhiro Miyazaki(Kyoto Univ. of Edu.)

On the Gorenstein property of the Ehrhart rings of some types of stable
set polytopes of a graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the Gorenstein property of the Ehrhart rings of some types of stable
set polytopes of a graph概 要 Let G = (V, E) be a finite simple graph. We denote by RV the set of maps from V to R and treat as the∑#V -dimensional Euclidean space. We set HSTAB(G) := {f ∈ RV | f (x) ≥ 0 for any x ∈ V , k∈K f (k) ≤ 1∑#C−1
for any clique K andfor any odd cycle C}, TSTAB(G) := {f ∈ RV | f (x) ≥ 0
c∈C f (c) ≤
2
∑
∑
#C−1
for any odd cycle C} andfor any x ∈ V ,x∈e f (e) ≤ 1 for any e ∈ E andc∈C f (c) ≤2∑
V
QSTAB(G) := {f ∈ R | f (x) ≥ 0 for any x ∈ V and k∈K f (k) ≤ 1 for any clique K}. In this talk, wegive criteria for the Gorenstein property of the Ehrhart rings of these convex polytopes.

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応用数学

10 梶 浦 大 起 (広 島 大 理)
松 本
眞 (広 島 大 理)
奥 田 隆 幸 (広 島 大 理)

Hiroki Kajiura (Hiroshima Univ.)
Makoto Matsumoto (Hiroshima Univ.)
Takayuki Okuda (Hiroshima Univ.)72

可換 association scheme 上の部分集合による積分誤差評価と diﬀerence
set の一般化 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Integration error bounds for a finite subset of commutative association
schemes and a generalization of diﬀerence sets.

概 要 Let X be a finite set, (X, {Ri }di=0 ) a commutative association scheme, ki its i-th valency, {Ej }dj=0 ⊂CX×X the primitive idempotents of its Bose–Mesner Algebra, and dj the rank of Ej . For a function
f : X → C, let fj be its j-th component (i.e. the convolution with Ej ). We define a (seemingly strange)
∑d
∑d √∑
2
norm
:= j=0j=0 fj √x∈X |fj (x)| dj . For a non-empty finite set Y , we denote by IY (f ) ∈ C
dim

the average of f over Y , and define the√integration error Err(f : Y ) := ∥IX (f ) − IY (f )∥. We show an error
bound supf ∈CX Err(f : Y )/∥f ∥√dim ≥1/#Y −1/#X, and prove that the equality holds if and only if Y
#X−1

is

“a diﬀerence set” in the association scheme. Here, the notion of “diﬀerence set” is a suitable generalizationof well-studied diﬀerence sets, from finite groups to association schemes.
11 梶 浦 大 起 (広 島 大 理)

Hiroki Kajiura (Hiroshima Univ.)

Diﬀerence set の association scheme への一般化と 2-design · · · · · · · · · · · 15
A generalization of diﬀerence sets to association schemes and 2-designs

概 要 Let G be a finite group. There is a notion of diﬀerence set in G, which is a subset Y ⊂ G. Bruck

proved that this notion is equivalent to that the G-orbit G · Y ⊂(G )kbeing a 2-design, where k = #Y .

We give a generalization of this result. We define a notion of diﬀerence set in an association scheme. If
the association scheme is the thin-scheme of a finite group G, this notion coincides with the original one.
Our main result is the following: if the association scheme is a Schurian association scheme (associatedwith a transitive action of G on a finite set X), then Y ⊂ X is a diﬀerence set (in our sense) if and only
( )if G · Y ⊂ X
k is a 2-design. We note that the original notion gives symmetric designs, but we have no
examples of symmetric designs by this generalization.
12 佐 竹 翔 平 (熊 本 大 先 端)

Shohei Satake (Kumamoto Univ.)

Almost diﬀerence set から得られる near-homogeneous tournament · · · · 15
Near-homogeneous tournaments from almost diﬀerence sets

概 要 A tournament is an oriented complete graph. Near-homogeneous tournaments proposed by Tabib(1980) are known as an important class of tournaments in the study of cycles in regular tournaments.
However, at present, there seem to be only few known examples and constructions.
In this talk, we establish a connection between near-homogeneous tournaments and almost diﬀerence setsin combinatorial design theory. This result, together with a construction of almost diﬀerence sets by Ding,
Helleseth and Lam (1999), provides a construction of a new family of near-homogeneous tournaments, whichcontains examples found by Astié-Vidal and Dugat (1990). Under a number-theoretic conjecture by Hardy
and Littlewood (1923), we also confirm a conjecture by Savchenko (2016).
15:45〜16:45
澤特別講演
正 憲 (神戸大システム情報)

Masanori Sawa

(Kobe Univ.)

Cubature 公式の構成理論とその数値解析・統計学への応用
The construction theory of cubature formulas with applications to numerical analysis and statistics

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73

応用数学

9 月 23 日（水）9:50〜12:00
13 安 藤清 (国 立 情 報 学 研 )Kiyoshi Ando(Nat. Inst. of Information)

Contractible edges in k-connected graphs with minimum degree greaterthan or equal to ⌊ 3k−1
2 ⌋ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Contractible edges in k-connected graphs with minimum degree greaterthan or equal to ⌊ 3k−1
2 ⌋概 要 Let G be a k-connected graph. An edge of G is said to be a k-contractible edge if the contraction ofit results in a k-connected graph. We denote by Ec (G) the set of k-contractible edges of G. We denote by
V (G) and δ(G) the set of vertices of G and the minimum degree of G, respectively. We prove that if k ≥ 3,
5k−5k
|V (G)| ≥ 2k + 1 and δ(G) ≥ ⌊ 3k−1
2 ⌋, then |Ec (G)| ≥ |V (G)| + ⌊ 2 ⌋⌈ 2 ⌉ − k. We also show that this resultis sharp.
14 藤 田 慎 也(横浜市大データサイエンス)(Univ. of Strathclyde)
S. Kitaev
佐 藤 静 佳 (横浜市大国際総合)
Li-Da Tong
(Nat. Sun Yat-sen Univ.)

Shinya Fujita (Yokohama City Univ.)
Sergey Kitaev (Univ. of Strathclyde)
Shizuka Sato (Yokohama City Univ.)
Li-Da Tong (Nat. Sun Yat-sen Univ.)

On properly ordered coloring of vertices in a vertex-weighted graph · · 10

On properly ordered coloring of vertices in a vertex-weighted graph概 要 We introduce the notion of a properly ordered coloring (POC) of a weighted graph, that generalizes

the notion of vertex coloring of a graph. Under a POC, if xy is an edge, then the larger weighted vertex
receives a larger color; in the case of equal weights of x and y, their colors must be diﬀerent. Further, fora graph G, we introduce the function f (G) which gives the maximum number of colors required by a POC
over all weightings of G. Another function we introduce is χP OC (G; t) giving the minimum number of colors
required over all weightings of G using t distinct weights.
In this talk, we present some results on this new parameter of a vertex-weighted graph.
15 R. J. Gould ( Emory Univ. )弘 畑 和 秀 (茨 城 工 高 専 )A. K. Rorabaugh (Univ. of Tennessee)

Ronald J. Gould (Emory Univ.)
Kazuhide Hirohata(Ibaraki Nat. Coll. of Tech.)Ariel Keller Rorabaugh(Univ. of Tennessee)

Vertex-disjoint chorded cycles and degree sum condition · · · · · · · · · · · · 10

Vertex-disjoint chorded cycles and degree sum condition

概 要 Let k be a positive integer. In 1963, Corradi and Hajnal proved that if G is a graph of order at least

3k and the minimum degree of G is at least 2k, then G contains k vertex-disjoint cycles. Finkel proved ananalogous result for chorded cycles, and Chiba et al. improved Finkel’s result. In this talk, we consider theextension of these results.

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応用数学

16 松 本 直 己 (慶 大 D M C)

Naoki Matsumoto (Keio Univ.)

74

グラフのゲーム染色数と染色数の差について · · · · · · · · · · · · · · · · · · · · · · · 10

On the diﬀerence between game chromatic number and chromatic number of graphs

概 要 The graph coloring game on a graph G is a two-player game. In the game, they alternately color an

uncolored vertex of G by a color in a given color set X so that any two adjacent vertices receive the diﬀerent
colors. The first player’s aim is to completely color all vertices of G only by using colors in X, and thesecond player’s aim is to avoid it. The game chromatic number of a graph G, denoted by χg (G), is theminimum number of colors such that Alice has a winning strategy for the graph coloring game on G. In
this talk, we introduce our recent result that for any simple graph G, χg (G) − χ(G) ≤ ⌊ n2 ⌋ − 1, where χ(G)is the chromatic number of G, where the estimation is best possible for any even n.
17 野 口 健 太 (東 京 理 大 理 工)

Kenta Noguchi (Tokyo Univ. of Sci.)

平面的グラフの proper orientation number · · · · · · · · · · · · · · · · · · · · · · · · 10

Proper orientation number of planar graphs

概 要 In this talk, we give some results about proper orientation number of planar graphs. Our main result

is as follows: Let G be a bipartite planar graph with δ(G) ≥ 3. Then the proper orientation number of G
is at most 3. Both of the bounds in this theorem are tight.
18 前 澤 俊 一 (横浜国大環境情報) ♭ グラフに全域 k-tree が存在するための禁止部分グラフペア · · · · · · · · · · · 15
小 関 健 太 (横浜国大環境情報)
Shunichi Maezawa
A forbidden pair for the existence of spanning k-trees in graphs(Yokohama Nat. Univ.)
Kenta Ozeki (Yokohama Nat. Univ.)
概 要 For an integer k ≥ 2, a k-tree is a tree with maximum degree at most k. A k-tree containing allvertices of a graph G is called a spanning k-tree of G. In 2010, Ota and Sugiyama gave a forbidden subgraphcondition for a graph to have a spanning k-tree and they posed a conjecture that is stronger than theirresult. We solved their conjecture.
19 阿 部 敏 生 (横浜国大環境情報)
小 関 健 太 (横浜国大環境情報)
Seog-Jin Kim ( Konkuk Univ. )Toshiki Abe (Yokohama Nat. Univ.)
Kenta Ozeki (Yokohama Nat. Univ.)
Seog-Jin Kim (Konkuk Univ.)

Alon–Tarsi number of K5 -minor-free graphs · · · · · · · · · · · · · · · · · · · · · · · 15

Alon–Tarsi number of K5 -minor-free graphs

概 要 Alon–Tarsi number is one of the invariant of graphs and it is an upper bound of chromatic number,list chromatic number and painting number. In this talk, we will introduce the following three theorems
and their applications. Let G be a K5 -minor-free graph. Then Alon–Tarsi number of G is at most 5, there
exists a matching M of G such that the Alon–Tarsi number of G − M is at most 4, and there exists a forest
F such that the Alon–Tarsi number of G − E(F ) is at most 3.
20 中 本 敦 浩 (横浜国大環境情報)
飛 鷹 郁 弥 (横浜国大環境情報)
Atsuhiro Nakamoto(Yokohama Nat. Univ.)
Fumiya Hidaka (Yokohama Nat. Univ.)

Quadrangulations of a polygon with spirality · · · · · · · · · · · · · · · · · · · · · · 15
Quadrangulations of a polygon with spirality

概 要 A polygon P on the plane is a cycle with several straight segments. A quadrangulation of P is ageometric plane graph with vertex set V (P ) such that the outer cycle coincides with P and each inner faceis quadrangular. In our talk, we discuss whether a given polygon P can be quadrangulated by adding edges
to the interior of P , introducing the notion called “spirality”.

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75

応用数学

21 中 本 敦 浩 (横浜国大環境情報)
池 上 大 稀 (横浜国大環境情報)
Atsuhiro Nakamoto(Yokohama Nat. Univ.)
Daiki Ikegami (Yokohama Nat. Univ.)

閉曲面上の三角形分割における対角変形の回数について · · · · · · · · · · · · · 15

The number of diagonal flips in triangulations on closed surfaces

概 要 In our talk, we prove that for any surface F 2 , there exists an integer N (F 2 ) such that any two n-vertex

triangulations on F 2 can be transformed into each other by O(n) diagonal flips, if n ≥ N (F 2 ). Moreover,
we improve the known bound for N (F 2 ).

9 月 24 日（木）9:00〜12:00
22 大 林 一 平(理化学研 AIP・東北大 AIMR)
吉 脇 理 雄(理化学研AIP・阪市大数学研・京大高等研)

Ippei Obayashi (RIKEN/Tohoku Univ.)
Michio Yoshiwaki(RIKEN/Osaka City Univ./Kyoto Univ.)

Field choice problem on persistent homology · · · · · · · · · · · · · · · · · · · · · · 15

Field choice problem on persistent homology

概 要 In this presentation, I will talk about the problem of the choice of a coeﬃcient field on persistenthomology. When we compute a persistence diagram, we need to select a coeﬃcient field before computation.
We should understand the dependency of the diagram on the coeﬃcient field for the better computationand interpretation of the diagram. We give some suﬃcient and necessary conditions for the independenceof the diagram to the coeﬃcient field. We also give an eﬃcient algorithm to determine whether a given
input satisfies the condition or not. The algorithm is already implemented in HomCloud, our data analysis
software based on persistent homology. The software will be helpful for data analysis using persistenthomology.
23 平 岡 裕 章(京大高等研・理化学研 AIP)
吉 脇 理 雄(理化学研AIP・京大高等研・阪市大数学研)

Yasuaki Hiraoka (Kyoto Univ./RIKEN)
Michio Yoshiwaki(RIKEN/Kyoto Univ./Osaka City Univ.)

ジグザグパーシステント加群に対する代数的安定性定理 · · · · · · · · · · · · · 15

Algebraic stability theorem for zigzag persistence modules

概 要 The algebraic stability theorem is an important part of the stability theorem in the theory of persistenthomology and guarantees that the persistence diagram is stable with respect to small changes in the given
persistence module. For purely zigzag persistence modules, an algebraic stability theorem also holds (Botnan
and Lesnick). In contrast with their strategy, our strategy focuses on the equivalence of derived categories ofordinary and (not necessarily purely) zigzag persistence modules, and hence we derive an algebraic stability
theorem for zigzag persistence modules from the ordinary ones. This enables us to obtain an algebraic
stability theorem for the wider class than the result of Botnan and Lesnick. In this talk, we will discuss analgebraic stability theorem for zigzag persistence modules and its derived category.

最終版: 2020/08/22
応用数学

24 E. G. Escolar(理化学研 AIP・京大高等研)
K. F. Meehan (京 大 高 等 研)
吉 脇 理 雄(理化学研AIP・阪市大数学研・京大高等研)
Emerson Gaw Escolar(RIKEN / Kyoto Univ.)
Killian F. Meehan (Kyoto Univ.)
Michio Yoshiwaki(RIKEN/Osaka City Univ./Kyoto Univ.)

76eEvery pair of Λ-interleavings are Λ-interleaved· · · · · · · · · · · · · · · · · · · · · 15eEvery pair of Λ-interleavings are Λ-interleaved

概 要 There is an isometry theorem relating the interleaving distance between 1D persistence modules andthe bottleneck distance of the corresponding barcodes. The bottleneck distance is defined by matchings
between the barcodes, and can be seen as a “diagonal” interleaving of the persistence modules. We wish
to study how far arbitrary interleavings are from “diagonal” interleavings. To that end, we work in amore general setting of prosets. We introduce the concept of a shoelace of a proset, and show thatthe representation category of the shoelace is isomorphic to the category of interleavings. Through this,we can formulate interleavings between interleavings. Finally, we show that any two Λ-interleavings areee is a “twisted” interleaving on the shoelace naturally induced from Λ.
Λ-interleaved,
where Λ25 中 島健 (理 化 学 研 AIP)
浅 芝 秀 人 (静 岡 大 理)
E. G. Escolar(理化学研 AIP・京大高等研)
吉 脇 理 雄(理化学研AIP・京大高等研・阪市大数学研)(RIKEN)
Ken Nakashima(
Hideto Asashiba Shizuoka Univ.)
Emerson Gaw Escolar(RIKEN / Kyoto Univ.)
Michio Yoshiwaki(RIKEN/Kyoto Univ./Osaka City Univ.)

On approximation of 2D persistence modules by interval-decomposables· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On approximation of 2D persistence modules by interval-decomposables

概 要 In this work, we propose a new invariant for 2D persistence modules called the compressed multiplicity

and show that it generalizes the notions of the dimension vector and the rank invariant. In addition, we
propose an “interval-decomposable approximation” δ ∗ (M ) of a 2D persistence module M . In the case that
M is interval-decomposable, we show that δ ∗ (M ) = M . Furthermore, even for representations M notnecessarily interval-decomposable, δ ∗ (M ) preserves the dimension vector and the rank invariant of M .
大理) ♭ マルチパラメータパーシステントホモロジーの分解論における極限定理
26 清 水 超 貴 (京平 岡 裕 章 (京 大 高 等 研)
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Tatsuki Shimizu (Kyoto Univ.)
Yasuaki Hiraoka (Kyoto Univ.)

Limit theorems in the decomposition theory of multi-parameter persistent homology

概 要 In the decomposition theory of the multi-parameter persistence modules, which is a multidimensionalversion of the usual 1D persistence modules, there exists an algebraic diﬃculty unlike the 1D case. Rather
than solving this diﬃculty purely algebraic, we attempt to tackle the diﬃculty probabilistically, that is,considering a scaling limit with an appropriate scale. As a first step, we have shown that there exists a
scaling limit of rank invariant, and that of multiplicities of irreducible representations in a representation of
a commutative ladder obtained from a point process.

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応用数学

27 宮
平
金
角

大
理)
永
潤 (京
岡 裕 章 (京 大 高 等 研 )澤秀 (京 大 高 等 研 )大理)
田 謙 吉 (阪Jun Miyanaga (Kyoto Univ.)
Yasuaki Hiraoka (Kyoto Univ.)
Shu Kanazawa (Kyoto Univ.)
Kenkichi Tsunoda (Osaka Univ.)

ランダム方体複体過程のパーシステント図に対する大偏差原理について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Large deviation principle for persistence diagrams of random cubicalcomplex processes

概 要 Recently, multi-scale topological features of weighted higher-dimensional cubes, have been studied via

persistence diagrams in various application fields such as digital image processing. In this talk we showa large deviation principle for the histograms generated by the average frequency densities on subdivision
rectangles of persistence diagram. Furthermore, constructing a suitable projective limit using linear mapsthat average among the values on subdivisions rectangles, we show that the sequence of the histograms
ordered by size of rectangle also satisfies a large deviation principle as elements in the projective limit.
28 金 澤秀 (京 大 高 等 研 )Shu Kanazawa(Kyoto Univ.)

ランダム単体複体の Betti 数に対する大数の法則 · · · · · · · · · · · · · · · · · · · · 15

Law of large numbers for Betti numbers of random simplicial complexes

概 要 The Erdős–Rényi graph model has been extensively studied since the 1960s as a typical random graphmodel. Recently, the study of random simplicial complexes has drawn attention as a higher-dimensional
generalization of random graphs. In this talk we introduce a class of homogeneous and spatially independent
random simplicial complexes, and discuss the asymptotic behavior of their Betti numbers. This result
extends the law of large numbers for Betti numbers of Linial–Meshulam complexes obtained in an earlier
study by Linial and Peled. A key element in the argument is the local weak convergence of simplicial
complexes. Inspired by the work of Linial and Peled, we establish the local weak limit theorem forhomogeneous and spatially independent random simplicial complexes.
29 見 上 達 哉 (京大理)Tatsuya Mikami (Kyoto Univ.)

結晶格子における最速浸透問題 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

First passage percolation on crystal lattices

概 要 First passage percolation (FPP) model is a time evolution version of the bond percolation model:

each edge in the cubic lattice is assigned a random passage time, and consider the behavior of percolation
region B(t), which consists of the vertices that can be arrived from the origin within a time t > 0. Cox andDurrett (1981) showed the shape theorem for the region, saying that the normalized region B(t)/t converges
to some limit shape. The aim of this study is a generalization of the FPP model to the model formulated
on general crystal lattices, and a general version of the shape theorem is obtained. A comparison of thelimit shapes obtained from two crystal lattices with covering relation is also studied.

最終版: 2020/08/22
応用数学

30 E. G. Escolar(理化学研 AIP・京大高等研)
平 岡 裕 章 (京 大 高 等 研)
伊 神
満 (イ ェ ー ル 大)
Y. Ozcan(MIT Sloan・FTI Consulting)Emerson Gaw Escolar(RIKEN / Kyoto Univ.)
Yasuaki Hiraoka (Kyoto Univ.)(Yale Univ.)
Mitsuru Igami
Yasin Ozcan(MIT Sloan / FTI Consulting)78

Mapping firms’ locations in technological space: A topological analysis
of patent statistics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Mapping firms’ locations in technological space: A topological analysis
of patent statistics

概 要 Where do firms innovate? Locating and visualizing them in technological space is challenging, because

it is high-dimensional and unstructured. We address this issue by using a method in topological data analysis
called Mapper, which combines local clustering with global reconstruction. We apply this method to a panelof 333 major firms’ patent portfolios in 1976–2005 in 430 technological areas and propose a definition of thecharacteristic “flares” that appear in the Mapper graph. Results suggest the Mapper graph captures salient
patterns in firms’ patenting histories, and the type and length of flares are correlated with firms’ financial
performances in a statistically and economically significant manner.
31 宇 田 智 紀 (東 北 大 A I M R)
Tomoki Uda(Tohoku Univ.)

異なるグリッド形状での劣位集合合併木間の interleaving 距離の評価 · · 12Interleaving distance on merge trees of grid data sublevelsets on diﬀerent
grid topologies

概 要 0-dimensional persistent homology of a sublevelset filtration over a grid, called a merge tree, is usefulin certain applications in image processing and topological flow data analysis. As it is well-kwown thatstability holds true by interleaving distance, merge trees are robust to noises and hence in harmony withdata analysis. However, there were no such concrete knowledge of how underlying grid topology aﬀect a
resulting merge tree. In this presentation I will show the upper bound estimate of interleaving distance ofmerge trees where underlying grid topologies vary under certain assumptions.
32 若 生 将 史 (神戸大システム情報)
Masashi Wakaiki (Kobe Univ.)

Robustness of strong stability with respect to sampling · · · · · · · · · · · · · 15
Robustness of strong stability with respect to sampling

概 要 We study the following question: “Suppose that an infinite-dimensional continuous-time system witha state-feedback controller is strongly stable. If we transform this continuous-time controller into a sampleddata controller by adding an idealized sample-and-hold process, will the resulting sampled-data system bestrongly stable for all suﬃciently small sampling periods?” We show that the answer of this question is“yes” under certain assumptions, by using the so-called Arendt–Batty–Lyubich–Vu theorem.

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応用数学

14:15〜16:30
33 坂 口 文 則 (福 井 大 工)Fuminori Sakaguchi (Univ. of Fukui)

どこまで拡がる?微分方程式整数型解法の適用範囲 —整数の四則演算だ
けでどこまでできるか— · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A possibility of wider application of an algorithm for solving ODEs bymeans only of four arithmetical operations among integers

概 要 A kind of generalization was proposed by the author for an integer-type algorithm for solving higher-

order linear ODEs, which was proposed by the author and M. Hayashi several years ago, by means ofalgebraic extensions of the field of rational functions. By this generalization, for example, we can solve
the higher-order linear ODEs whose coeﬃcient functions are general algebraic functions, by means only offour arithmetical operations among integers. In this study, we show that the range of application of thisalgorithm can be expanded into a spacial class of the cases where the coeﬃcient functions of ODEs involve
exponential, trigonometric and hyperbolic functions. Moreover, some successful numerical examples are
given for ODEs whose coeﬃcient functions involve, for example, sigmoid and tangent functions.
34 松 井 一 徳 (金 沢 大 自 然)

Kazunori Matsui (Kanazawa Univ.)

Dirichlet 型の圧力境界条件を課した Navier–Stokes 方程式に対する射影法について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Projection methods for the Navier–Stokes equation with boundary conditions of Dirichlet type on the pressure

概 要 Most studies on projection methods, which are numerical schemes for solving the time-dependent

Navier–Stokes equation, deal with Dirichlet boundary conditions for the velocity and Neumann ones for thepressure on the whole boundary. However, boundary conditions involving the pressure are important for
real-world applications. We propose new projection methods with the pressure boundary conditions andshow the stability for the solution to the schemes and establish error estimates in suitable norms.
35 劉

雪 峰 (新 潟 大 自 然 )Xuefeng Liu(Niigata Univ.)

ポアソン方程式の有限要素解の各点値の誤差評価 · · · · · · · · · · · · · · · · · · · 15

Pointwise error estimation for finite element solution to boundary value
problems with O(h2 ) convergence rate

概 要 The hypercircle method and the idea of Kato–Fujita’s method are applied to develop a point-wiseerror estimation for FEM solutions to boundary value problems. It is shown that one can give explicit lower
and upper bound for the solution value at an interior point with an O(h2 ) convergence rate.
36 土 屋 卓 也 (愛 媛 大 理)
柏 原 崇 人 (東 大 数 理 )Takuya Tsuchiya (Ehime Univ.)
Takahito Kashiwabara (Univ. of Tokyo)

異方的三角形分割上でもロバストな不連続 Galerkin スキーム · · · · · · · · · 15

A robust discontinuous Galerkin scheme on anisotropic meshes

概 要 Discontinuous Galerkin (dG, in short) methods are extensions of usual (Ritz–)Galerkin finite element

methods that are much more flexible on meshes to use. However, when we deal with dG methods, wemust impose the shape-regularity condition on meshes for both theoretical error analysis and practicalcomputations. In this paper, we present a new symmetric interior penalty discontinuous Galerkin schemewith a modified penalty term. We show that, without imposing the shape-regularity condition on meshes,
the new dG scheme inherits all good properties from the standard dG methods. Numerical experiments
confirm the theoretical error estimates obtained.

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応用数学

37 緒 方 秀 教 (電通大情報理工)
Hidenori Ogata(Univ. of Electro-Comm.)80

二重周期的ポテンシャル流問題に対する代用電荷法 · · · · · · · · · · · · · · · · · 15

Method of fundamental solutions for the problem of doubly-periodic
potential flow

概 要 We propose a method of fundamental solutions (MFS) for the problem of two-dimensional potential

flow past a doubly-periodic array of obstacles. It is diﬃcult to apply the conventional MFS to this problem
because the solution involves a doubly-periodic function. We propose a new type of MFS, where the solution
is approximated by a linear combination of the periodic fundamental solutions expressed by the complex
logarithmic functions and the theta functions. Numerical examples show the eﬀectiveness of our method.
38 村 川 秀 樹 (龍谷大先端理工)
R. Bairo(Imperial Coll. London)
J. A. Carrillo (Univ. of Oxford)
M. Schmidtchen (Sorbonne Univ.)

Hideki Murakawa (Ryukoku Univ.)
Rafael Bairo (Imperial Coll. London)José A. Carrillo (Univ. of Oxford)
Markus Schmidtchen (Sorbonne Univ.)

非線形非局所 Fokker–Planck 型方程式に対するエネルギー散逸有限体積
スキーム · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Energy-dissipating finite-volume scheme for nonlinear nonlocal Fokker–
Planck type equations

概 要 We deal with a nonlinear nonlocal Fokker–Planck type equation, which appears in various fields

of application. The equation has some properties; the property of mass conservation, non-negativity,
boundedness and the energy-dissipation property. In this talk, we introduce and analyze a numerical
scheme that preserves these properties at the discrete level.
39 渡 部 善 隆(九大情報基盤研究開発センター)
木 下 武 彦(九大情報基盤研究開発センター)
中 尾 充 宏 (早 大 理 工)

Yoshitaka Watanabe (Kyushu Univ.)
Takehiko Kinoshita (Kyushu Univ.)
Mitsuhiro T. Nakao (Waseda Univ.)

Hilbert 空間における線形作用素に対する可逆性検証の効率化とその応用· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

An eﬃcient approach for verifying the existence of inverse of linear operators in Hilbert spaces and its applications

概 要 In this talk we describe some numerical verification procedures to prove the invertibility of a linear

operator in Hilbert spaces and to compute a bound for the norm of its inverse. These approaches improve on
previous procedures that use an orthogonal projection of the Hilbert space and its a priori error estimations.
Several verified examples which confirm the eﬀectiveness of the new procedures are presented.
40 木 下 武 彦(九大情報基盤研究開発センター)
橋 本 弘 治 (中 村 学 園 大)
中 尾 充 宏 (早 大 理 工)

Takehiko Kinoshita (Kyushu Univ.)
Kouji Hashimoto(Nakamura Gakuen Univ.)
Mitsuhiro T. Nakao (Waseda Univ.)

非線形放物型方程式の解の検証における初期値分離型評価の包含効果抑制について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the decreasable eﬀect of wrapping eﬀect using a priori estimates separating initial values in the verification probrem for parabolic equations

概 要 The verification procedures of solutions for initial value problem have an expanding phenomenonof varidated area called wrapping eﬀect. We will propose a new verification procedure of solutions forparabolic initial-boundary value problem to reduce wrapping eﬀect using a priori estimates separating theheat equation with initial values and the shifted equation without initial values.

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応用数学

16:45〜17:45

特別講演

尾 崎 克 久(芝浦工大システム理工)

行列積に対するエラーフリー変換: 基礎・応用・未来

Katsuhisa Ozaki(Shibaura Inst. of Tech.)Error-free transformation for matrix multiplication: Basic, applications,and future

概 要 This talk concerns the numerical computations of matrix multiplication. Floating-point numbers andfloating-point arithmetic defined in IEEE 754 are widely used in numerical computations. The performanceof the numerical computation is very high. On the other hand, the problem of rounding errors is crucial. We
proposed an error-free transformation of matrix multiplication. The matrix product is transformed into an
unevaluated sum of floating-point matrices. This technique is useful for accurate numerical computations.
Besides, the error-free transformation is applied to interval matrix multiplication and generation of test
matrices in numerical linear algebra. Moreover, we can develop reproducible numerical algorithms and afast algorithm for matrix multiplication using low precision arithmetic on GPGPU based on the error-freetransformation.

9 月 25 日（金）9:00〜11:45
通大)41 山 本 野 人 (電(通大)新 田 光 輝 電
Nobito Yamamoto(Univ. of Electro-Comm.)
Koki Nitta (Univ. of Electro-Comm.)

非双曲型平衡点近傍での局所 Lyapunov 関数の精度保証法による構成 · · 15

Construction of local Lyapunov functions around non hyperbolic equilibria by verified computation

概 要 We propose new methods to construct local Lyapunov functions around non-hyperbolic equilibria

using verified computation. The methods are based on the normal form theory in dynamical systems.
42 内 海 晋 弥 (学 習 院 大 理)

Shinya Uchiumi (Gakushuin Univ.)

曲線で囲まれた領域におけるラプラシアンの固有値の包含について · · · · 15

Guaranteed bounds for the eigenvalues of Laplacian in curved domains

概 要 We consider the eigenvalue problem of the Laplacian with the homogeneous Dirichlet boundary

condition, or homogeneous Neumann condition, in curved domains. Based on the theorem by Liu andOishi, we show guaranteed bounds of the eigenvalues, where the lower and upper bounds are explicitly
computable. We use the curved finite element space by Zlámal. The constant that appears in the theorem
by Liu and Oishi is estimated by using the argument by Ciarlet and Raviart.
43 高 安 亮 紀 (筑波大システム情報)( Boston Univ. )J. Jaquette

Akitoshi Takayasu (Univ. of Tsukuba)
Jonathan Jaquette (Boston Univ.)

Homoclinics and global existence of solutions to a quadratic nonlinear
Schrödinger equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Homoclinics and global existence of solutions to a quadratic nonlinear
Schrödinger equation

概 要 In this talk, we show global existence of solutions to a quadratic nonlinear Schrödinger equation. For

the nonliear Schrödinger equation without Gauge-invariance global existence of solutions is less apparent
due to the lack of conserved quantities. By using a scaling technique based on a solution of ordinary
diﬀerential equations, our main theorem gives a suﬃcient condition of global existence of such a solution.
The proof is obtained by rigorous numerics, via rigorous numerical integration of the solution and validating
the suﬃcient condition based on interval arithmetic.

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応用数学

82

♭
44 石 渡 哲 哉
確率微分方程式に対する正値性保存スキーム · · · · · · · · · · · · · · · · · · · · · · · 10
(芝浦工大システム理工)
安 孫 子 啓 介 (芝 浦 工 大 理 工)
Tetsuya Ishiwata
Positivily preserving scheme for stochastic diﬀerential equations(Shibaura Inst. of Tech.)
Keisuke Abiko (Shibaura Inst. of Tech.)概 要 In this talk, we introduce positivity preserving numerical method based on Ito’s formula. In thisabstract, we only denote our idea for 1 dimensional problems, but our ideas can easily be extended tomulti-dimensional problems.
45 石 渡 哲 哉(芝浦工大システム理工)長 瀬 准 平 (芝 浦 工 大 理 工)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)Jumpei Nagase (Shibaura Inst. of Tech.)

深層ニューラルネットの接続構造と有限次元モデルの表現能力 · · · · · · · · 10

Connection structure of deep neural networks and expressive power offinite dimensional models

概 要 In this talk, we mainly compare the structures of ResNet and DenseNet with a view to systematicallyunderstand the skip connection which is one of the structure of the model. As a result, it was theoreticallyconfirmed that it is only due the regularity of full connected layers that gives diﬀerences in the expressive
power of both models.
46 寺 川 峻 平 (神戸大システム情報)
松 原
崇 (阪 大 基 礎 工)
谷 口 隆 晴 (神戸大システム情報)

Shunpei Terakawa (Kobe Univ.)
Takashi Matsubara (Osaka Univ.)
Takaharu Yaguchi (Kobe Univ.)

ニューラル常微分方程式の学習における離散化手法の学習可能性解析 · · 15

Learnability of numerical integrators for neural ordinary diﬀerential
equations

概 要 Recently, methods for learning diﬀerential equation models from data using neural networks havebeen actively studied. In this talk, we propose a theoretical framework for the analysis of the influence ofnumerical integrators that are used to discretize the diﬀerential equation model in learning.
47 坂 上 貴 之 (京大理)Takashi Sakajo (Kyoto Univ.)

トーラス面上の定常渦 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Vortex equilibria on the surface of a torus

概 要 We are concerned with vortex dynamics on the surface of a torus. Although the flows on the surface

of a torus is no longer a physical relevance to real fluid flow phenomena, it is theoretically interesting toobserve whether the geometric nature of the torus, i.e., a compact, orientable 2D Riemannian manifoldwith non-constant curvature and one handle, yields diﬀerent vortex dynamics that are not observed so far.
In this presentation, we show two equilibrium states of vortex structures. One is called vortex crystals, inwhich point vortices are moving in the longitudinal direction without changing their relative configuration.
Another one is an exact analytic solution of a modified Liouville equation on the toroidal surface, which is
known as Stuart vortex.
48 関 坂 歩 幹 (明大研究・知財) ♭ 星間ガスのジーンズ不安定性とダイナミクス · · · · · · · · · · · · · · · · · · · · · · · 15
Ayuki Sekisaka(Meiji Univ.)

The Jeans instability and dynamics in the nebula model of compressive
viscous gases

概 要 The Jeans instability is a key concept that facilitates our understanding of galaxy and star formation inastrophysics. To understand this dynamics, we consider the dynamics of the three-dimensional compressible
Navier–Stokes–Poisson system.

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49 中 田 行 彦 (青 学 大 理 工)
( Univ. Szeged )G. VasYukihiko Nakata(Aoyama Gakuin Univ.)
Gabriella Vas (Univ. Szeged)

ステップ型の非線形性をもつ分布型の遅延微分方程式 · · · · · · · · · · · · · · · 15

A distributed delay diﬀerential equation with a step-type nonlinearity

概 要 In this presentation, we consider a distributed delay diﬀerential equation. It has been shown that

there exists a periodic solution with a minimum period of 2 for a certain type of equations. We study thedelay diﬀerential equation when the nonlinear function is given by a step function. Convergence of thesolution to the periodic solution and the existence the periodic solutions are studied.
♭
2 次元遅延微分方程式系の周期解の安定性について · · · · · · · · · · · · · · · · · · 1050 石 渡 哲 哉(芝浦工大システム理工)
A. Eremin(Saint Petersburg State Univ.)
石 渡 恵 美 子 (東 京 理 大 理 )中 田 行 彦 (青 学 大 理 工 )Tetsuya Ishiwata(Shibaura Inst. of Tech.)Alexey Eremin(Saint Petersburg State Univ.)
Emiko Ishiwata (Tokyo Univ. of Sci.)
Yukihiko Nakata(Aoyama Gakuin Univ.)

Stability of periodic solutions to 2 dimensional delay diﬀerential equation

概 要 We discuss 2 dimensional delay diﬀerential equation with a constant delay. This system has blow-

up solutions and infinitely many periodic solutions. In this talk, we show the stability of these periodic
solutions.
51 村 田 実 貴 生 (東 京 農 工 大 工)
Mikio Murata(Tokyo Univ. of Agri. and Tech.)

Max 型拡散セル・オートマトンのチューリング不安定性解析 · · · · · · · · · 15
Analysis of Turing instability in max function type diﬀusion cellular
automata

概 要 As basic cellular automata that express the reaction-diﬀusion phenomenon, we proposed “max function

type diﬀusion cellular automata”. In this presentation, we give the definition of Turing instability in themax function type diﬀusion cellular automata and analyze the Turing instability of the max function
type diﬀusion cellular automata. In addition, we discuss the similarities and diﬀerences with the Turing
instability of the reaction-diﬀusion equation.
14:15〜15:15
52 渡 辺樹 (早 大 理 工 )Itsuki Watanabe (Waseda Univ.)

Limit theorems for a space-homogeneous nonlocal diﬀusion with nonlinear reactions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Limit theorems for a space-homogeneous nonlocal diﬀusion with nonlinear reactions

概 要 We discuss the diﬀerence of two mathematical models of nonlocal diﬀusion; the deterministic andstochastic models. The deterministic model is given by a nonlinear reaction-diﬀusion equation, and thestochastic model is given by a multi-dimensional jump Markov process. In this talk, we show two convergence
theorems. First, we prove that the diﬀerence of two models converges to 0 in probability. Second, we
consider the rescaled diﬀerence and prove that it converges to some stochastic process in distribution on the
Skorokhod space.

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応用数学

53 中 村 健 一 (金 沢 大 理 工)
日 吉 将 大 (金 沢 大 自 然)
山 崎 貴 史 (金 沢 大 自 然)

Ken-Ichi Nakamura (Kanazawa Univ.)
Masahiro Hiyoshi (Kanazawa Univ.)
Takafumi Yamazaki (Kanazawa Univ.)

84

Speed of traveling waves for discrete bistable Lotka–Volterra competition system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Speed of traveling waves for discrete bistable Lotka–Volterra competition system

概 要 We study a Lotka–Volterra competition-diﬀusion system with bistable nonlinearity in which thehabitat is divided into discrete niches. We derive a condition that the propagation failure phenomenon
occurs. We also derive suﬃcient conditions for the existence of traveling waves with nonzero speed. By
these results, we can predict which species will become dominant and win the competition.
大⋆)54 西 浦 廉 政 (北Shuangquan Xie (東 北 大 A I M R)
T. Kolokolnikov (Dalhousie Univ.)

Yasumasa Nishiura (Hokkaido Univ.⋆)
Shuangquan Xie (Tohoku Univ.)
Theodore Kolokolnikov(Dalhousie Univ.)

Complex oscillatory motion of multiple spikes for a three-component
Schnakenberg model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Complex oscillatory motion of multiple spikes for a three-component
Schnakenberg model

概 要 We introduce a three-component Schnakenberg model. A key feature is that it has a solution consistingof N spikes that undergoes a Hopf bifurcation with respect to N distinct modes nearly simultaneously. This
results in complex oscillatory dynamics of the spikes, not seen in typical two-component models. We derivea reduced equations of motion which consist of coupled ordinary diﬀerential equations of order 2N around
Hopf bifurcation points. We also apply the method of multiple scales to the resulting ODEs to derive along-time dynamics. For instance, the coexistence of stable in-phase and out-of-phase modes, which does notoccur for two-component systems, is observed for two-spike case. Further away from the Hopf bifurcation
points, we observe numerically a variety of highly complex oscillatory modes including chaotic motions.
55 長 山 雅 晴 (北 大 電 子 研)
大理)
佐 藤 優 祐 (北(中 田
聡 広 島 大 理)

Masaharu Nagayama (Hokkaido Univ.)
Yusuke Satoh (Hokkaido Univ.)
Satoshi Nakata (Hiroshima Univ.)

自励往復運動する自己駆動体に対する数理モデリング · · · · · · · · · · · · · · · 15

Mathematical modeling for a self-inverted reciprocation of a self-propelledmaterial

概 要 We construct a mathematical model for a butyl salicylate (BS) droplet motion to clarify the emergencemechanism for the mode-change of a droplet motion depending on the surfactant concentration in the waterphase. Our model is composed of reaction-diﬀusion equations for a sodium dodecyl sulfate (SDS), BS, andthe mixture of SDS and BS, and an equation on motion for the BS droplet. Features of reciprocation andmode-change depending on the concentration of SDS are qualitatively reproduced by numerical calculation
based on an equation of motion and the kinetics of SDS and BS at the air/aqueous interface.

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応用数学

15:30〜16:30
李特別講演
聖 林 (広 島 大 理 )Sungrim Seirin Lee (Hiroshima Univ.)「現象–数理–数学」を繋ぐ反応拡散方程式

Pattern formation in life sciences and reaction-diﬀusion equation

概 要 Since A. Turing’s landmark paper (1952), reaction-diﬀusion equations became a symbol of mathemat-

ical model for pattern formation in life science. A short-range self-activation and long-range inhibition havebeen considered as a fundamental mechanism by which a symmetry breaking is triggered and a pattern,
namely, non-constant steady state, is formed in reaction-diﬀusion systems. And many mathematical models
in pattern formation also have based on it. However, once we take a step back and look at the truly
pure essence of reaction-diﬀusion equation(s), i.e. reaction and diﬀusion, we can find more potential ofreaction-diﬀusion equation(s) and see various patterning dynamics in a simple reaction-diﬀusion equation(s)without a basis of activation-inhibition chemical reactions. In this talk, I will introduce such unlimited
potentials of reaction-diﬀusion equation(s) as a pattern forming system which have been done by myself
during theses 10 years. I also would like to discuss how mathematical modeling (or mathematical modeler)in life science and pure mathematics (or pure mathematician) can be collaborated and open a new trail ofapplied mathematics.

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トポロジー

ト

ポ

ロ

ジ

86

ー

9 月 22 日（火）10:00〜12:00
1 花 木
良 (岐 阜 大 教 育)
Ryo Hanaki(Gifu Univ.)

結び目の影の肥沃性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On fertility of knot shadows

概 要 A knot K is a parent of a knot H if there exists a minimal crossing diagram D of K such that asubset of the crossings of D can be changed to produce a diagram of H. A knot K with crossing number
n is fertile if for any prime knot H with crossing number less than n, K is a parent of H. We introduce
fertile for a knot shadow which is a diagram without over/under information at all crossings. We show that
if an alternating knot K is fertile then the crossing number of K is less than eight.
2 鎌 田 直 子 (名 古 屋 市 大 理)

Naoko Kamada (Nagoya City Univ.)

Almost classical virtual links · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Almost classical virtual links

概 要 Classical link diagrams admit Alexander numberings. However some virtual link diagrams do not

admit Alexander numberings. If a virtual link diagram admits an Alexander numbering, it is said to bealmost classical. A virtual link is almost classical if it has an almost classical virtual link diagram. In
this talk, we introduce a map from the set of virtual link diagrams to that of almost classical virtual link
diagrams. This map induces a map from the set of virtual links to that of almost classical virtual links.
3 大 山 淑 之 (東 京 女 大 数 理)
櫻 井 み ぎ 和 (芝 浦 工 大 工)
Yoshiyuki Ohyama(Tokyo Woman’s Christian Univ.)
Migiwa Sakurai(Shibaura Inst. of Tech.)

A construction of infinitely many virtual knots with properties of Kishino’s
knot · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
A construction of infinitely many virtual knots with properties of Kishino’sknot

概 要 Satoh and Taniguchi defined a virtual knot invariant Jn called the n-writhe for each non-zero integer

n. The n-writhes give the coeﬃcients of some polynomial invariants for virtual knots including the index
polynomial, the odd writhe polynomial and the aﬃne index polynomial. It is obvious that the virtualizationof a real crossing is an unknotting operation for virtual knots. The unknotting number by the virtualization
is called the virtual unknotting number. Kishino’s knot is a virtual unknotting number one knot which has
the trivial n-writhes and the trivial Jones polynomial. In this talk, we construct infinitely many virtual
knots with the same properties as Kishino’s knot. By using the Miyazawa polynomial, we showed that thesevirtual knots are non-trivial and non-classical, and their knot types are all diﬀerent.
4 宮 澤 治 子
(津田塾大数学・計算機研)
大理)
和 田 康 載 (阪
大
商)
安 原
晃 (早

Haruko Miyazawa (Tsuda Coll.)(Osaka Univ.)
Kodai Wada(
WasedaUniv.)
Akira Yasuhara

絡み目の Dabkowski–Sahi 不変量と 4-move · · · · · · · · · · · · · · · · · · · · · · · · 10

The Dabkowski–Sahi invariant and 4-moves for links

概 要 Dabkowski and Sahi defined an invariant of a link in the 3-sphere, which is preserved under 4-moves.

This invariant is a quotient of the fundamental group of the complement of the link. It is generally diﬃcult todistinguish the Dabkowski–Sahi invariants of given links. In this talk, we give a necessary condition for the
existence of an isomorphism between the Dabkowski–Sahi invariant of a link and that of the corresponding
trivial link. Using this condition, we provide a practical obstruction to a link to be trivial up to 4-moves.

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トポロジー

5 水 澤 篤 彦 (早 大 非 常 勤 )小 鳥 居 祐 香 (理化学研・阪大理)

Atsuhiko Mizusawa (Waseda Univ.)
Yuka Kotorii (RIKEN/Osaka Univ.)

Clasper を用いた, 2 つの 4 成分 link が link-homotopic であるか判定する
アルゴリズム · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
An algorithm which determine whether given two 4-component links arelink-homotopic

概 要 We give an algorithm to determine whether given two 4-component links are link-homotopic or not via

the clasper theory. This algorithm is a translation of Habegger and Lin’s algorithm. We describe actionsof partial conjugates to 4-component string links explicitly.
6 石 井 一 平
中 村 拓 司 (山 梨 大 教 育 )斎 藤 敏 夫 (上 越 教 育 大 )Ippei Ishii
Takuji Nakamura (Univ. of Yamanashi)
Toshio Saito (Joetsu Univ. of Edu.)

A coloring invariant of 3-manifolds derived from flow spines and virtual
knot diagrams · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
A coloring invariant of 3-manifolds derived from flow spines and virtual
knot diagrams

概 要 Let M be a closed, oriented, connected 3-manifold. Considering the homotopy class of its non-singular

vector field, we obtain a flow spine of M and, furthermore, construct a virtual knot diagram from the flow
spine. This talk introduces a coloring invariant of 3-manifolds by using their virtual knot diagrams. Our
invariant distinguishes the Poincaré homology sphere from the 3-sphere.
7 市 原 一 裕 (日 大 文 理 )斎 藤 敏 夫 (上 越 教 育 大 )鄭仁 大 (近 畿 大 理 工 )T. W. Mattman(California State Univ., Chico)Kazuhiro Ichihara (Nihon Univ.)
Toshio Saito (Joetsu Univ. of Edu.)(Kindai Univ.)
In Dae Jong
Thomas W. Mattman(California State Univ., Chico)Two-bridge knots admit no purely cosmetic surgeries · · · · · · · · · · · · · · · 15

Two-bridge knots admit no purely cosmetic surgeries

概 要 We show that two-bridge knots and alternating fibered knots admit no purely cosmetic surgeries,

i.e., no pair of distinct Dehn surgeries on such a knot produce 3–manifolds that are homeomorphic asoriented manifolds. Our argument, based on a recent result by Hanselman, uses several invariants of knots
or 3–manifolds; for knots, we study the signature and some finite type invariants, and for 3–manifolds, wedeploy the SL(2, C) Casson invariant.
8 中 江 康 晴 (秋 田 大 理 工 )市 原 一 裕 (日 大 文 理 )Yasuharu Nakae (Akita Univ.)
Kazuhiro Ichihara (Nihon Univ.)

種数 1 ファイバー結び目に沿ったデーン手術と基本群の左順序付け可能性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Dehn surgeries on genus one fibered knots and left-orderability of fundamental groups

概 要 We study Dehn surgeries along genus one fibered knots and which resultant manifolds have left-orderable fundamental groups. The 3-sphere has only two genus one fibered knots, the trefoil and thefigure-eight knot. In contrast with the 3-sphere, some lens spaces have more genus one fibered knots.
In 2014, Baker completely classified the number of genus one fibered knots in lens spaces. Along theclassification, we show that, on some class of such knots in lens spaces, all integral surgeries yield 3manifolds with left-orderable fundamental groups. In order to prove this theorem, we examine the existenceof Anosov flow whose stable / unstable foliation is R-covered in the resultant manifold.

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トポロジー

9 野 坂 武 史 (東 工 大 理)

Takefumi Nosaka (Tokyo Tech)

88

幾つかの 3 次元多様体の普遍被覆空間のセル複体 · · · · · · · · · · · · · · · · · · · 10

Cellular chain complexes of universal covers of some 3-manifolds

概 要 We consider a class of closed 3-manifolds, which satisfies “Property (†)”. For a 3-manifold M in thisclass, we give a presentation of the cellular chain complexes of the universal covers of M . The class includes
all surface bundles, some surgeries of knots in S 3 , some cyclic branched cover of S 3 , and some Seifert
manifolds. As an application, we establish a formula for calculating the linking form of a cyclic branchedcover of S 3 .
10 野 坂 武 史 (東 工 大 理)

Takefumi Nosaka (Tokyo Tech)

SL2 (R)-Casson 不変量とライデマイスタートーション · · · · · · · · · · · · · · · 15
An SL2 (R)-Casson invariant and Reidemeister torsions

概 要 We define an SL2 (R)-Casson invariant of closed 3-manifolds. Moreover, we describe a procedure forcomputing the invariant in terms of a Reidemeister torsion and discuss approaches to giving the Casson
invariant some gradings.
14:15〜15:15 特別講演
森 藤 孝 之 (慶 大 経 済)

Takayuki Morifuji (Keio Univ.)

双曲結び目・絡み目のねじれ Alexander 多項式

Twisted Alexander polynomials of hyperbolic knots and links

概 要 The twisted Alexander polynomial is defined for a pair consisting of the group and its representation.

It is a natural generalization of the Alexander polynomial and gives a powerful tool in the study of lowdimensional topology. Based on huge numerical calculations, Dunfield, Friedl and Jackson have proposed
a conjecture that the twisted Alexander polynomial associated to the holonomy representation determines
the genus and fiberedness of a hyperbolic knot. In this talk we will survey recent results on the conjectureand explain its generalization to hyperbolic links.

9 月 23 日（水）10:00〜11:40
11 大 森 源 城 (東 京 理 大 理 工)
阪 田 直 樹 (埼 玉 大 理 工)

Genki Omori (Tokyo Univ. of Sci.)
Naoki Sakata (Saitama Univ.)

種数 4 と 5 の場合の向き付け不可能曲面上の involution の Dehn twistcrosscap slide 表示について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Dehn twist-crosscap slide presentations for involutions on non-orientablesurfaces of genus 4 and 5

概 要 Lickorish proved that any element of the mapping class group of a non-orientable is a product of Dehn

twists and crosscap slides. We call the product a Dehn twist-crosscap slide presentation for the element.
In this talk, we give Dehn twist-crosscap slide presentations for all conjugacy classes of involutions on
non-orientable surfaces of genus 4 and 5. The Dehn twist-crosscap slide presentations are constructed byproducts of Szepietowski’s finite generating set.
12 野 崎 雄 太 (広島大先進理工)佐 藤 正 寿 (東京電機大未来)
鈴 木 正 明 (明 大 総 合 数 理)
Yuta Nozaki (Hiroshima Univ.)
Masatoshi Sato (Tokyo Denki Univ.)
Masaaki Suzuki (Meiji Univ.)

Abelian quotients of the Y -filtration on the homology cylinders via the
LMO functor · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Abelian quotients of the Y -filtration on the homology cylinders via the
LMO functor

概 要 We construct a series of homomorphisms on the Y -filtration on the homology cylinders via the modZ reduction of the LMO functor. The restriction of our homomorphism to the lower central series of theTorelli group does not factor through Morita’s refinement of the Johnson homomorphism. We use it toshow that the abelianization of the Johnson kernel of a closed surface has torsion elements. This is the joint
work with Masatoshi Sato and Masaaki Suzuki.

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トポロジー

13 谷 口 正 樹 (理化学研iTHEMS) ♭ 3 次元多様体の余次元 1 の埋め込みと Yang–Mills ゲージ理論 · · · · · · · · · 15
Masaki Taniguchi(RIKEN)

Codimension-1 embeddings of 3-manifolds and Yang–Mills gauge theory

概 要 We give a relation between existence of an embedding of a 3-manifold into a 4-manifold X andexistence of an irreducible SU(2)-representation of the fundamental group of X. For example, we can prove
the following result: Let X be a closed oriented definite 4-manifold containing the Poincare homology
3-sphere as a submanifold. Then the fundamental group of X admits at least four irreducible SU(2)representations. Since the Poincare homology 3-sphere has a (topological) locally flat embedding into the
4-space, the above result can not be proved in the topological category. The proof uses a quantitative
formulation of instanton Floer homology.
14 浅 野 喜 敬 (東 北 大 理)

Nobutaka Asano (Tohoku Univ.)

Vertical 3-manifolds in simplified genus 2 trisections of 4-manifolds · · · 15
Vertical 3-manifolds in simplified genus 2 trisections of 4-manifolds

概 要 A trisection is a decomposition of a closed 4-manifold by 3 tuple of 4-dimensional 1-handlebodies,

which was introduced by Gay and Kirby. They proved the existence of a trisection for any closed 4-manifold
by using a stable map (called a trisection map) from the 4-manifold to R2 . After their work, a simplified
trisection was introduced by Baykur and Saeki. They proved the existence of a simplified trisection froma simplified broken Lefschetz fibration. In this talk, we will give a classification of 3-manifolds that canbe obtained as the preimages of arcs on R2 by simplified genus 2 trisection maps, which we call vertical
3-manifolds.
15 河 村 建 吾 (工 学 院 大)Kengo Kawamura (Kogakuin Univ.)

Immersed 2-knot のスピン構成とその既約性 · · · · · · · · · · · · · · · · · · · · · · · 10
Spinning construction of immersed 2-knot and its irreducibility

概 要 Using a certain spinning construction producing immersed 2-knots, we give an infinite family ofirreducible immersed 2-knots with one self-intersection point.
16 安 部 哲 哉 (立 命 館 大 理 工) ♭ Table of annulus presentations of knots · · · · · · · · · · · · · · · · · · · · · · · · · · · 10産
大)田 神 慶 士 (水Tetsuya Abe (Ritsumeikan Univ.)
Keiji Tagami (Nat. Fisheries Univ.)

Table of annulus presentations of knots

概 要 In this talk, we determine which knots have special annulus presentations of knots up to 8-crossings.

We also give explicit pictures of special annulus presentations of knots up to 8-crossings.
大理)
17 鎌 田 聖 一 (阪
(
)
阪
大
理・
JSPS
B. BodeSeiichi Kamada (Osaka Univ.)
Benjamin Bode (Osaka Univ./JSPS)

On knotted surfaces as vanishing sets of polynomials · · · · · · · · · · · · · · · 10
On knotted surfaces as vanishing sets of polynomials

概 要 This is an announcement of the results of the paper “Knotted surfaces as vanishing sets of polynomials”,

arXiv: 2004.02468. We provide an algorithm that constructs for any element B of the loop braid group apolynomial f : R5 → R2 such that the vanishing set f −1 (0) ∩ S 4 on the unit 4-sphere contains a set that isambient isotopic to the closure of B. We also provide an algorithm that constructs for any spinning braid
B in C × S 1 × S 1 there exists a holomorphic polynomial f : C3 → C such that f −1 (0) ∩ (C × S 1 × S 1 ) isambient isotopic to B. Our algorithms also provide an upper bound on the degree of f .

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トポロジー

大
理)
18 鎌 田 聖 一 (阪A. Bartholomew ( Univ. Sussex )( Univ. Sussex )R. Fenn
鎌 田 直 子 (名 古 屋 市 大 理)

Seiichi Kamada (Osaka Univ.)
Andrew Bartholomew (Univ. Sussex)(Univ. Sussex)
Roger Fenn
Naoko Kamada (Nagoya City Univ.)90

On doodles and commutator identities · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On doodles and commutator identities

概 要 This is an announcement of our paper “Doodles and commutator idintities”.

A doodle diagram is a collection of immersed circles in the 2-sphere whose multiple points are transverse
double points. A colored doodle diagram with a noose system determines a commutator identity (anidentity among commutators). We discuss doodles with proper noose systems and elementary commutator
identities. In particular we show that there is a bijection between cobordism classes of colored doodles andweak equivalence classes of elementary commutator identities.
13:15〜14:15

2020 年度日本数学会幾何学賞受賞特別講演 (幾何学分科会と合同)
枡 田 幹 也 (阪 市 大 理) ♭ トーリックトポロジーにおけるコホモロジー剛性問題

Mikiya Masuda (Osaka City Univ.)

Cohomological rigidity problem in toric topology

概 要 A toric variety is a normal complex algebraic variety with an algebraic action of a C*-torus having an

open dense orbit. The fundamental theorem in toric geometry says that there is a one-to-one correspondence
between toric varieties and fans. Among toric varieties, compact smooth toric varieties, which we call toric
manifolds, are well understood. For instance, their cohomology rings and Chern classes are explicitly
described in terms of the associated fans. The classification of toric manifolds as varieties reduces to theclassification of the associated fans. However, the classification of toric manifolds as smooth manifolds is
not well understood. Related to this, the author and Dong Youp Suh posed the following problem in 2008.
Cohomological rigidity problem (for toric manifolds). Are toric manifolds diﬀeomorphic (or homeomorphic)
if their cohomology rings with integer coeﬃcients are isomorphic as graded rings?
Many partial aﬃrmative solutions to the problem have been obtained but no counterexamples are known
so far. There are several analogues of the problem and two of them are a symplectic analogue and a real
analogue. The former is related to McDuﬀ’s question on the uniqueness of a toric structure on a monotone
symplectic manifold and the latter is related to flat Riemannian manifolds and hyperbolic 3-manifolds ofLoebell type. In this talk, I will overview some development on these problems.

9 月 24 日（木）10:00〜11:55
19 佐 藤 尚 倫 (早 大 理 工)

Takamichi Sato (Waseda Univ.)

Isomorphism between the stabilizers of finite sets of numbers in the R.
Thompson group F · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Isomorphism between the stabilizers of finite sets of numbers in the R.
Thompson group F

概 要 Let HU be the subgroups of the R. Thompson group F that are stabilizers of finite sets U of numbersin the interval (0, 1) under the natural action of F on (0, 1). In this talk we give a necessary and suﬃcientcondition for HU and HV to be isomorphic for finite sets U and V .

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トポロジー

20 近 藤 博 文 (二宮高)

Hirofumi Kondo(Ninomiya High School)

A Nullstellensatz for ideals of C ∞ functions in dimension 2 · · · · · · · · · · 15
A Nullstellensatz for ideals of C ∞ functions in dimension 2

概 要 Suppose that an ideal J of C ∞ functions on an open subset of R2 is a Lojasiewicz ideal. We describe

the set of C ∞ functions vanishing on the zeros of J explicitly using J in an open neighborhood of each pointin zeros of J, it can be obtained by taking real radical and closure starting from J repeatedly for a finite
number of times. This gives an another aﬃrmative answer to Bochnak’s conjecture in dimension 2, which
is first done by Risler.
21 越 野 克 久 (神 奈 川 大 工)

Katsuhisa Koshino (Kanagawa Univ.)

The topological type of a function space on a metric measure space with
the Lp norm · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The topological type of a function space on a metric measure space with
the Lp norm

概 要 Let X be a metric measure space which satisfies the following conditions: 1. X is separable andlocally compact, 2. all Borel subsets of X are measurable and for any measurable set E ⊂ X, there exists a
Borel set B ⊂ X such that E ⊂ B and B \ E is a null set, 3. each non-empty open set U ⊂ X has positive
measure, 4. every compact set K ⊂ X has finite measure, 5. X \ {x ∈ X | {x} is measurable and null} is
not dense in X. In this talk, we shall show that the space of real-valued uniformly continuous functions on
X with the Lp norm, 1 ≤ p < ∞, is homeomorphic to the subspace consisting of sequences conversing to 0
in the pseudo interior.
22 北 澤 直 樹 (九 大 I M I)

Naoki Kitazawa (Kyushu Univ.)

4 次元空間への折り目写像の構成で得られる 7 次元単連結閉多様体の無限族 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Infinitely many 7-dimensional closed and simply-connected manifolds
via construction of explicit fold maps into the 4-dimensional Euclideanspace

概 要 Closed and simply-connected diﬀerentiable manifolds are central geometric objects in classical diﬀer-

ential topology. They were classified via algebraic and abstract objects, thanks to the assumption that thedimensions are suﬃciently high. However, due to this it is diﬃcult to understand them in geometric andconstructive ways. In this talk, we will show a related study via construction of Morse functions and foldmaps, which are higher dimensional versions of Morse functions. We present infinitely many 7-dimensional
closed and simply-connected manifolds and explicit fold maps into the 4-dimensional Euclidean space.
Note that since the discovery of exotic spheres by Milnor in 1956, the class of 7-dimensional closed andsimply-connected manifolds has been an attractive class for a long time.
23 丸 山 修 平 (名 大 多 元 数 理)

Shuhei Maruyama (Nagoya Univ.)

ポアンカレの回転数と円板のシンプレクティック微分同相群上の擬準同型· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Poincaré’s rotation number and quasi-morphisms on symplectomorphismgroups of the disk

概 要 On symplectomorphism groups of the disk, we construct two homogeneous quasi-morphisms which

relate to the Calabi invariant and the flux homomorphism respectively. We also give the relation between
the quasi-morphisms and Poincaré’s rotation number.

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トポロジー

24 松 雪 敬 寛 (東 大 数 理)

Takahiro Matsuyuki (Univ. of Tokyo)

92

モデル障害類と Milnor–Wood 不等式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Obstraction class for higher homotopy algebra models and Milnor–Woodinequality

概 要 We introduced obstruction classes for the simplicial bundle of homotopy algebra models associatedwith a fiber bundle. It is an invariant for a fiber bundle. On the other hand, it is known that these exists
a certain inequality for Euler class of flat bundles. In our research, we attempt to prove such an inequality
for our obstruction class. In this presentation, we present this attempt and some results.
25 野 沢啓 (立 命 館 大 理 工) ♭ リーマン葉層構造のヘフリガーコホモロジーについて · · · · · · · · · · · · · · · 15

Hiraku Nozawa (Ritsumeikan Univ.)

Haefliger cohomology of complete Riemannian foliations概 要 Haefliger characterized taut foliations in terms of so-called Haefliger cohomology. We show that

Haefliger cohomology characterizes strongly tense foliations, namely, foliated manifolds which admit a
Riemannian metric such that the mean curvature form of the leaves is closed and basic. We show that
Haefliger cohomology is dual to invariant cohomology for complete Riemannian foliations. As an applicationof these results, we prove that any complete Riemannian foliation is strongly tense, which is a generalizationof Dominguez’s tenseness theorem for Riemannian foliations on closed manifolds.
26 中 井 洋 史 (東京都市大理工)工大⋆)
吉 村 善 一 (名Hirofumi Nakai (Tokyo City Univ.)
Zen-ichi Yosimura(Nagoya Inst. of Tech.⋆)

胞体数が少ないスペクトラムの実 Johnson–Wilson ホモロジー群 · · · · · · 15

Real Johnson–Wilson homology groups of spectra with a few cells

概 要 The real Johnson–Wilson theory is a general homology theory, established by Hu–Kriz and Kitchloo–

Wilson. It is not complex-oriented theory and is the higher analogue of real K-theory. The coeﬃcientgroups have been determined by Hu–Kriz and now we know that it has rich structures. It is importantsince it is expected to have rich information about the homotopy groups of spheres, for example. In thistalk, we will announce the results on the real Johnson–Wilson homology groups of small spectra, each ofwhich has a few cells.
14:15〜15:15

特別講演
A. Berglund (Stockholm Univ.) ♭ Characteristic classes of manifold bundles and graph homology

Alexander Berglund (Stockholm Univ.)

Characteristic classes of manifold bundles and graph homology

概 要 We introduce new families of rational characteristic classes of manifold bundles associated to homology

classes in a certain graph complex.
More precisely, we consider bundles of simply connected spaces where the fiber is a closed oriented manifold
and the structure group is the group of diﬀeomorphisms of the fiber that fix an embedded disk. The graphcomplex we consider is closely related to the Feynman transform of the Lie operad, the homology of which
is known to be expressible in terms of the homology of automorphism groups of free groups.
The new classes may be viewed as a generalization of the Miller–Morita–Mumford classes; we show thatthese may be recovered from zero dimensional graph homology. We also show that the new classes provide
a better understanding of the calculation of the stable rational cohomology of the block diﬀeomorphismgroup of the manifold ♯g S d × S d (the g-fold connected sum of S d × S d ) due to Ib Madsen and myself.

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無限可積分系

無 限

可

積

分

系

9 月 22 日（火）9:30〜12:00
1 神 吉 雅 崇 (関西大システム理工)

Masataka Kanki (Kansai Univ.)

ある多項間漸化式の代数的エントロピーについて · · · · · · · · · · · · · · · · · · · 15

The algebraic entropies of some multi-term recurrences

概 要 We will present a certain discrete dynamical system defined on an integer lattice. The system havethe coprimeness property, which is an algebraic analogue of the singularity confinement, while it is nonintegrable in terms of exponential degree growth. The system can be regarded as an extension to the
Hietarinta–Viallet type equation. We will derive (or conjecture for some cases) the algebraic entropies ofthe equations which is obtained by reductions from the system. This presentation is based on a joint workin a preprint arXiv: 1812.08923.
2 中 園 信 孝 (東 京 農 工 大 工 )(Univ. of Sydney)
N. JoshiNobutaka Nakazono(Tokyo Univ. of Agri. and Tech.)
Nalini Joshi (Univ. of Sydney)

Consistency around a cuboctahedron property · · · · · · · · · · · · · · · · · · · · · 15
Consistency around a cuboctahedron property

概 要 It is a natural question to ask when discrete versions of integrable systems are themselves integrable.

This question has led to very active and productive searches for partial diﬀerence equations that haveproperties closely related to those of integrable PDEs, such as the Korteweg–de Vries equation. Recent
results have focused on partial diﬀerence equations given by polynomial equations placed in a consistent
way on faces of cubes, which turn out to have the desired integrability properties. In this talk, we show an
extension of this search to cuboctahedra.
3 大 山 陽 介 (徳 島 大 理 工 )Yousuke Ohyama (Tokushima Univ.)

Asymptotic analysis of the third q-Painlevé equation · · · · · · · · · · · · · · · 15
Asymptotic analysis of the third q-Painlevé equation(1)

概 要 We study asymptotic expansion of the third q-Painlevé equation (A3 ) around the origin. We also

study the connection matrix corresponding the Lax pair of the third q-Painlevé equation.
4 田 所 勇 樹 (木 更 津 工 高 専 )関 口 昌 由 (木 更 津 工 高 専 )鎌 田
勝 (木更津工高専⋆)
Yuuki Tadokoro(Nat. Inst. of Tech., Kisarazu Coll.)
Masayoshi Sekiguchi(Nat. Inst. of Tech., Kisarazu Coll.)
Masaru Kamata(Nat. Inst. of Tech., Kisarazu Coll.⋆)

Nonlinear O(3) sigma model in discrete complex analysis · · · · · · · · · · · · 15

Nonlinear O(3) sigma model in discrete complex analysis

概 要 We study a discrete version of the two-dimensional nonlinear O(3) sigma model derived from discrete

complex analysis. We show the discrete version of an equality for the energy of this model.

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無限可積分系

5 平 出 耕 一 (愛 媛 大 理)
松 岡 千 博 (阪 市 大 工)
Koichi Hiraide (Ehime Univ.)
Chihiro Matsuoka (Osaka City Univ.)

94

複素エノン写像の力学系にあらわれる Stokes 的現象 · · · · · · · · · · · · · · · · 15

Stokes-like phenomena which appear in the dynamics of complex Henonmaps

概 要 We consider invariant curves for complex Henon maps associated with an eigenvalue, with absolutevalue not equal to one, of the derivative at a fixed point. By the method of Borel–Laplace transform,
we can construct pairs (xi (t), yi (t)) of functions, parameterizing the invariant curves. Such functions haveforms of asymptotic expansions. In this talk, we give a relation with classical functions, due to Poincaré,
represented by Taylor series, and state a connection structure among functions’ pairs (xi (t), yi (t)), which islike structures known as (nonlinear) Stokes phenomena in diﬀerential equations.
6 濱 中 真 志 (名 大 多 元 数 理)
(グ ラ ス ゴ ー 大)
C. Gilson
Shan-Chi Huang (名 大 多 元 数 理)
(グ ラ ス ゴ ー 大)
J. Nimmo

Masashi Hamanaka (Nagoya Univ.)
Claire Gilson (Univ. of Glasgow)
Shan-Chi Huang (Nagoya Univ.)
Jonathan Nimmo (Univ. of Glasgow)

Soliton solutions of noncommutative anti-self-dual Yang–Mills equations· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Soliton solutions of noncommutative anti-self-dual Yang–Mills equations

概 要 We present exact soliton solutions of anti-self-dual Yang–Mills equations for G = GL(N ) on noncom-

mutative Euclidean spaces in four-dimension by using the Darboux transformations. Generated solutions
are represented by quasideterminants of Wronski matrices in compact forms. We give special one-soliton
solutions for G = GL(2) whose energy density can be real-valued. We find that the soliton solutions are thesame as the commutative ones and can be interpreted as one-domain walls in four-dimension. Scattering
processes of the multi-soliton solutions are also discussed.
7 濱 中 真 志 (名 大 多 元 数 理)
Shan-Chi Huang (名 大 多 元 数 理)

Masashi Hamanaka (Nagoya Univ.)
Shan-Chi Huang (Nagoya Univ.)

反自己双対 Yang–Mills 方程式のドメイン・ウォール型ソリトン解 · · · · · 15

Soliton solutions of domain-wall type to anti-self-dual Yang–Mills equations

概 要 We study exact soliton solutions of anti-self-dual Yang–Mills equations for G = GL(2) in four-

dimensional spaces with the Euclidean, Minkowski and Ultrahyperbolic signatures and construct special
kinds of one-soliton solutions whose action density (Lagrangian density) can be real-valued. These solitons
are shown to be new type of domain walls (not instantons) in four dimension by explicit calculationof the real-valued action density. Our results are successful applications of the Darboux transformation
developed by Nimmo, Gilson and Ohta. More surprisingly, integration of these action densities over the
four-dimensional spaces would not be infinity but zero. Furthermore, whether gauge group G = U (2) canbe realized on our solition solutions or not is also discussed on each real space.
8 筧三 郎 (立 教 大 理)

Saburo Kakei(Rikkyo Univ.)

格子ソリトン方程式と戸田階層 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Toda lattice hierarchy and soliton equations on square lattice

概 要 Lattice soliton equations of KdV-family and Boussinesq-family are investigated from the viewpointof the Toda lattice hierarchy. As a consequence, special solutions such as soliton solutions and algebrogeometric solutions are constructed in a unified manner.

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95

無限可積分系

14:30〜16:30(ブルゴーニュ大)9 N. Babinet
木 村 太 郎 (ブルゴーニュ大)Nicolas Babinet (Univ. de Bourgogne)
Taro Kimura (Univ. de Bourgogne)

超行列模型の量子スペクトル曲線と広田型微分方程式 · · · · · · · · · · · · · · · 15

Quantum curve for supermatrix model and Hirota diﬀerential equations

概 要 We quantize the spectral curve appearing in the saddle point analysis of the supermatrix model. We

show that the Hirota bilinear equation is obtained as a quantum curve equation instead of the usual ODE. In
particular for the Gaussian case, it is identified with that for the Painlevé IV τ function in Noumi–Yamada’s
symmetric form.
10 中 島啓 (東 大 I P M U )Hiraku Nakajima (Univ. of Tokyo)

Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum aﬃne
algebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum aﬃne
algebras概 要 We prove the conjecture by Gyenge, Neḿethi and Szendrői in arXiv:1512.06844, arXiv:1512.06848

giving a formula of the generating function of Euler numbers of Hilbert schemes of points Hilbn (C2 /Γ) on asimple singularity C2 /Γ, where Γ is a finite subgroup of SL(2). We deduce it from the claim that quantum
dimensions of standard modules for the quantum aﬃne algebra associated with Γ at ζ = exp(2πi/2(h∨ + 1))
are always 1, which is a special case of a conjecture by Kuniba [Kun93]. Here h∨ is the dual Coxeter
number. We also prove the claim, which was not known for E7, E8 before.
11 中 野 弘 夢 (東 北 大 理) ♭ 正の有理レベルにおける Fock 加群の構造について · · · · · · · · · · · · · · · · · · 15

Hiromu Nakano (Tohoku Univ.)

The structure theorem of Fock modules at positive rational level

概 要 We study structure of Fock modules at positive rational level. Using deformation theory constructedby Tuschiya–Wood and Shiraishi’s theorem for singular vectors of Fock modules, we proved the structure
theorem of Fock modules without Jantzen Filtration.
12 水 野 勇 磨 (東工大情報理工) ♭ クラスター代数から生じる差分方程式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Yuma Mizuno(Tokyo Tech)Diﬀerence equations arising from cluster algebras

概 要 We characterize Y/T-system type diﬀerence equations arising from cluster algebras by triples ofmatrices, which we call T-data, that have a certain symplectic property. We show that all mutation loops
are essentially obtained from T-data, which generalizes the general solution for period 1 quivers given by
Fordy and Marsh.
13 行 田 康 晃 (名 大 多 元 数 理)

Yasuaki Gyoda (Nagoya Univ.)

団複体の整合性次数 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Compatibility degree of cluster complexes

概 要 I will introduce a new function on the set of pairs of cluster variables, which we call it the compatibility

degree (of cluster complexes). The compatibility degree which I deal with in this talk is a generalizationof the “classical” compatibility degree introduced by Fomin and Zelevinsky. The classical one defines thegeneralized associahedra, and it is used to give the classification of cluster algebras of finite type. Cao andLi generalized this degree to that of cluster complexes by using d-vectors. We give another generalizationby using f -vectors on the basis of their studies. This is joint work with Changjian Fu.

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無限可積分系

14 西 山 雄 太 (熊 本 大 自 然)

Yuta Nishiyama (Kumamoto Univ.)

96

Macdonald 多項式の内積値とその組合せ論 · · · · · · · · · · · · · · · · · · · · · · · · 15
Inner products of Macdonald polynomials and its combinatorics

概 要 The Macdonald polynomials are a family of symmetric polynomials indexed by partitions. By calcu-

lating the inner product of the Macdonald polynomials corresponding to the partition (1n ), one obtains an
identity of two parameters. In this talk, we introduce its proof through constructing certain bijections bytransforming the Young diagrams of partitions. We also introduce similar identities obtained from innerproducts of other symmetric polynomials.

9 月 23 日（水）10:30〜11:30

特別講演

渡 邉 英 也 (京 大 数 理 研)

ı 量子化

Hideya Watanabe (Kyoto Univ.)ıquantization

概 要 ıquantum groups are generalizations of quantum groups appearing as one-sided coideal subalgebras ofquantum groups in the theory of quantum symmetric pairs. Representation theory of ıquantum groups play
important roles in various branches of mathematics and mathematical physics such as harmonic analysis,
integrable system, low-dimensional topology, and categorification. Recently, many results which we should
call “ıquantization” have been reported. ıquantizations have two meanings; (1) generalizing what is known
for usual quantum groups to ıquantum groups, (2) quantizing what is known for classical Lie algebras but
cannot be quantized by usual quantum groups, by means of ıquantum groups. In this talk, I introduce
examples of ıquantizations such as canonical basis, geometric construction, Hall algebraic construction,
Gelfand–Tsetlin basis of type B/D, Schur duality of type B/C/D, highest weight theory, canonical basis,and crystal basis.
13:15〜14:15

特別講演
斉 藤 義 久 (立 教 大 理) ♭ 楕円 Artin 群について

Yoshihisa Saito (Rikkyo Univ.)

On elliptic Artin groups

概 要 In the study of representation theory of Lie groups and Lie algebras, the regular Weyl group orbit

spaces and their fundamental groups (called Artin groups or generalized braid groups) have quite importantroles.
In the middle of 80’s, motivated by the study of singularity theory, Kyoji Saito introduced the notion of
elliptic root systems, and study their basic properties. Especially, he introduced an “elliptic analogue” ofthe regular Weyl group orbit spaces, so-called the elliptic regular orbit spaces, and study their detailed
structure in algebraic and diﬀerential geometrical point of view.
In this talk, we study the fundamental groups of the regular elliptic Weyl group orbit spaces. These groups
are presented by a generator system associated with the elliptic diagrams, and we call them the elliptic Artin
groups. Furthermore, some basic properties of these groups will be also discussed. Especially, the elliptic
regular orbit space is defined over the moduli space of elliptic curves. This fact leads us to the descriptionof the elliptic modular group actions on elliptic Artin groups. This talk is based on a joint work with Kyoji
Saito.