Abstract
Jan. 25 (Mon)
9:00 – 10:00 Kentaro Nakamura (Saga university)
Zeta morphisms for rank two universal deformations.
Abstract. In his work on the Iwasawa main conjecture for elliptic Hecke eigen cusp
newforms, Kazuya Kato constructed a map which we call the zeta morphism whose target
is the Iwasawa cohomology of the associated p-adic Galois representations. Combining
Fukaya-Kato’s idea for constructing the zeta morphisms for Hida families with many
deep results in the p-adic (local and global) Langlands correspondence for GL2/Q , weextend this map for the universal deformations of odd absolutely irreducible mod p Galois
representations of rank two. As an application, we prove a theorem, which roughly says
that, under some µ = 0 assumption, the Iwasawa main conjecture (without p-adic Lfunction) for one modular form implies the same conjecture for arbitrary congruent
modular forms.
10:30 – 11:30 Kenichi Namikawa (Kyushu University)
A cohomological interpretation of the period integrals for GL(3)×GL(2).
Abstract. The study of periods is fundamental for the arithmetic properties of Lfunctions, especially constructions of p-adic L-functions. Januszewski constructed p-adicRankin-Selberg L-functions for GL(n+1)×GL(n), however there are still several properties such as the choice of periods to be improved in his construction according to Coatesand Perrin-Riou’s conjecture. In this talk, we introduce a reﬁnement of RaghuramShahidi’s Whittaker periods in GL(3)×GL(2) case, and we give an explicit relation
between the periods, certain cohomology classes and critical values of Rankin-Selberg
L-functions for GL(3)×GL(2). We also discuss a motivic background of the periods
and its application to Januszewski’s interpolation formulas. This is a joint work withTakashi Hara.
13:00 – 14:00 Kazuki Morimoto (Kobe University)
On Ichino-Ikeda type formula of Bessel period for (SO(5), SO(2)).
Abstract. When SO(2) is non-split, we prove an explicit formula relating Bessel periodsfor (SO(5), SO(2)) and central L-values (Ichino-Ikeda type formula) for any irreducible
tempered cuspidal automorphic representations of SO(5) and SO(2). As an application,
we show generalized Böcherer conjecture which is an explicit formula relating certain
weighted sums of Fourier coeﬃcients and central L-values. This is a joint work with
Masaaki Furusawa(Osaka City University).

14:30 – 15:30 Hiroshi Noguchi (Kyoto University)
On genuine characters of the metaplectic group of SL2 (o) and thetafunctions.
Abstract. Let F be a totally real number ﬁeld and oF the ring of integers of F . Fengstudied when there exists a theta function which is a half-integral weight Hilbert modular
form of SL2 (oF ). In the case weight 1/2, she constructs theta functions. We determine
completely when there exists a theta function which is a half-integral weight Hilbert
modular form of SL2 (oF ). In order to prove this, we determine the genuine characters^of the metaplectic group SL
2 (o), where o is the ring of integers of a local ﬁeld.
16:00 – 17:00 (UTC 7:00 – 8:00) Toby Gee (Imperial College London)
Moduli stacks of (ϕ, Γ)-modules.
Abstract. I will review some properties of the moduli stacks of (ϕ, Γ)-modules which I
recently constructed with Matthew Emerton, and their connection to the weight part ofSerre’s conjecture.
Jan. 26 (Tue)9:00 – 10:00 (EST 19:00 – 20:00, 25 (Mon)) Chao Li (Columbia University)
The Beilinson-Bloch conjecture for unitary Shimura varieties.
Abstract: For certain automorphic representations π on unitary groups, we show that
if L(s, π) vanishes to order one at the center s = 1/2, then the associated π-localized
Chow group of a unitary Shimura variety is nontrivial. This proves part of the BeilinsonBloch conjecture for unitary Shimura varieties, which generalizes the BSD conjecture.
Assuming the modularity of Kudla’s generating series of special cycles, we further provea precise height formula for L′ (1/2, π). This proves the conjectural arithmetic innerproduct formula, which generalizes the Gross-Zagier formula to Shimura varieties ofhigher dimension. We will motivate these conjectures and discuss some aspects of theproof. This is joint work with Yifeng Liu.
10:30 – 11:30 (PST 17:30 – 18:30, 25 (Mon)) Ellen Eischen (University of Oregon)
Spin p-adic L-functions for GSp6 .
Abstract. I will discuss a construction of Spin p-adic L-functions of ordinary cuspidal
automorphic representations of GSp6 associated to Siegel modular forms. This is joint
work with G. Rosso and S. Shah.
13:00 – 14:00 Hirotaka Kakuhama (Kyoto University)
On the formal degree conjecture for inner forms of Sp4 and GSp4 .
Abstract: For a square integrable irreducible representation of a reductive group over a
local ﬁeld, Hiraga-Ichino-Ikeda conjectured that the formal degree is described in termsof the Langlands parameter (formal degree conjecture). On the other hand, for inner
forms of Sp4 and GSp4 , the Langlands correspondence is available. More precisely, theLanglands parameter is deﬁned via the theta correspondence with other groups for which
the Langlands correspondence has been established. In this talk, I introduce the formal
degree conjecture, a result on behavior of the formal degree under theta correspondence,
and a result on the formal degree conjecture for inner forms of Sp4 and GSp4 .

14:30 – 15:30 Koichi Takase (Miyagi University of Education)
On supercuspidal representations of Sp2n and Langlands parameters.
Abstract: I will speculate the Langlands parameters of explicitly constructed supercuspidal representations of Sp2n (F ) by means of checking -the formal degree conjecture,and -the root number conjecture.
15:30 – 15:40 On the RIMS workshop and Hakuba for the conference nextacademic.
Jan. 27 (Wed)9:00 – 10:00 (CST 18:00 – 19:00, 26 (Tue)) Matthew Emerton (The University ofChicago.)
Moduli stacks of Galois representations.
Abstract: In recent years, the formal deformation theory of Galois representations has
been extended in various contexts to a theory of moduli stacks of Galois representations,in which the Galois representations vary in a genuinely algebraic (rather than merelyformal) fashion. I will describe some ideas related to moduli stacks of Galois representations, and their relationship to the theory of automorphic forms. The talk will touchupon joint work of the speaker and Toby Gee, and also on work of Xinwen Zhu (someongoing jointly with the speaker, and some with Gee as well), as well as on the workand ideas of many other mathematicians.
10:30 – 11:30 Yoichi Mieda (The University of Tokyo)
Local Saito-Kurokawa A-packets and l-adic cohomology of Rapoport-Zink
tower for GSp(4).
Abstract: The Rapoport-Zink tower for GSp(4) is a p-adic local counterpart of the Siegel
threefold. Its l-adic cohomology is naturally equipped with actions of three groups: theWeil group of Qp , GSp4 (Qp ), and an inner form J(Qp ) of GSp4 (Qp ). These actions are
expected to be strongly related with the local Langlands correspondence, but they are
not fully understood yet. In this talk, I will focus on a certain class of non-tempered
local A-packets of J(Qp ), called the Saito-Kurokawa type. Under the assumption that
the A-packet contains a supercuspidal representation with trivial central character, I will
determine how the A-packet and the associated L-packet contribute to the cohomologyof the Rapoport-Zink tower for GSp(4). This is a joint work with Tetsushi Ito.

13:00 – 14:00 Hiroshi Ishimoto (Kyoto University)
A proof of Ibukiyama’s Shimura type conjecture on Siegel modular formsof half-integral weight and of degree 2.
Abstract: Ibukiyama’s Shimura type conjecture asserts that there is a linear isomorphism
between ”a space of vector valued Siegel cusp forms of degree 2 and of integral weight”
and ”a plus space of vector valued Siegel cusp forms of degree 2 and of half-integral
weight” which preserves L-functions. We can prove this conjecture by using Arthur’smultiplicity formula on the split odd special orthogonal group SO5 , Gan-Ichino’s multiplicity formula on the metaplectic group Mp4 , and the representation theory of theJacobi groups.
14:30 – 15:30 (13:30 – 14:30 in Singapore time) Wee Teck Gan (National University ofSingapore)
Nontempered Restriction Problems for Classical Groups.
Abstract. I will discuss an extension of the Gross-Pasad conjectures to the setting ofnontempered A-packets, mention some progress and highlight some subtleties in thenontempered setting. This is joint work with Gross and Prasad.
16:00 – 17:00 (UTC 7:00 – 8:00) Pol van Hoften (King’s College London)
Mod p points on Shimura varieties of parahoric level.
Abstract. The conjecture of Langlands-Rapoport gives a conjectural description of themod p points of Shimura varieties, with applications towards computing the (semisimple) zeta function of these Shimura varieties. The conjecture was proven by Kisin for
abelian type Shimura varieties at primes of (hyperspecial) good reduction, after having
constructed smooth integral models. For primes of (parahoric) bad reduction, Kisin andPappas have constructed ”good” integral and the conjecture naturally generalises to thissetting. In this talk I will discuss recent results towards the conjecture for these integral
models, under minor hypothesis, building on earlier work of Zhou. Along the way we will
see irreducibility results for various stratiﬁcations on special ﬁbers of Shimura varieties,including irreducibility of central leaves and Ekedahl-Oort strata.
Jan. 28 (Thu)
9:00 – 10:00 (PST 16:00 – 17:00, 27 (Wed)) Aaron Pollack (University of California,San Diego)
Singular modular forms on exceptional groups.
Abstract: The exceptional group E7,3 has a symmetric space with Hermitian tube structure. On it, Henry Kim wrote down low weight holomorphic modular forms that are”singular” in the sense that their Fourier expansion has many terms equal to zero. The
symmetric space associated to the exceptional group E8,4 does not have a Hermitianstructure, but it has what might be the next best thing: a quaternionic structure andassociated ”modular forms”. I will explain the construction of singular modular forms
on E8,4 , and the proof that these special modular forms have rational Fourier expansions,in a precise sense. This builds oﬀ of work of Wee Teck Gan and uses key input from
Gordan Savin.

10:30 – 11:30 (EST 20:30 – 21:30, 27 (Wed)) Naomi Tanabe (Bowdoin College)
Non-vanishing of central values of Rankin-Selberg L-functions.
abstract: It is believed that the central values of modular L-functions are non-vanishingunless there is an arithmetical reason for them to vanish. In this talk, we discuss someresults on the non-vanishing of central values of L-functions, with a special focus on thatof Rankin-Selberg L-functions attached to (Hilbert) modular forms. Key ingredients inthe proof are to establish asymptotics of certain twisted moments. This is a joint workwith Alia Hamieh.
13:00 – 14:00 Yota Maeda (Kyoto University)
On the Kodaira dimension of unitary Shimura varieties.
Abstract. The Kodaira dimension of Shimura varieties has been studied by many people. Kondo, Gritsenko-Hulek-Sankaran and Ma showed that certain orthogonal Shimuravarieties related with the moduli spaces of K3 surfaces are of general type by using theBorcherds lift. On the other hand, Gritsenko-Hulek proved some orthogonal Shimuravarieties are uniruled. In this talk, we consider similar problems for unitary Shimuravarieties. We give some suﬃcient conditions for general type or uniruledness of unitary
Shimura varieties in terms of Hermitian forms by using the Borcherds form and reﬂective modular forms. Moreover, we construct Hermitian lattices satisfying the above
conditions.
14:30 – 15:30 Hiraku Atobe (Hokkaido University)
The Zelevinsky-Aubert duality for classical groups.
Abstract: In 1980, Zelevinsky studied representation theory for p-adic general linear
groups. He gave an involution on the set of irreducible representations, which exchanges
the trivial representation with the Steinberg representation. Aubert extended this involution to p-adic reductive groups, which is now called the Zelevinsky-Aubert duality.
It is expected that this duality preserves the unitarity. In this talk, we explain an algorithm to compute the Zelevinsky-Aubert duality for odd special orthogonal groups orsymplectic groups. This is a joint work with Alberto Minguez in University of Vienna.
16:00 – 17:00 (UTC 7:00 – 8:00) Tobias Berger (The University of Sheﬃeld)
Eisenstein cohomology and CM congruences.
Abstract. This is a report on joint work in progress with Adel Betina (Vienna) toprove congruences between Eisenstein and cuspidal cohomology classes for imaginary
quadratic ﬁelds. I plan to discuss applications to R = T theorems and congruences forclassical CM modular forms.

Jan. 29 (Fri)9:00 – 10:00 (PST 16:00 – 17:00, 28 (Thu)) Sug Woo Shin (University of California,Berkeley)
Cohomology of Igusa varieties.
Abstract. I will review the deﬁnition of Igusa varieties in the context of Shimura varieties of Hodge type, and then survey results on the cohomology of Igusa varieties withapplications to arithmetic and geometric problems. This includes a recent project with
Arno Kret on computing H 0 .
10:15 – 11:15 Masao Oi (Kyoto University, Hakubi center)
Twisted endoscopic character relation for Kaletha’s regular supercuspidal
L-packets.
Abstract: Recently Kaletha constructed the local Langlands correspondence (i.e., Lpackets and their L-parameters) for a wide class of supercuspidal representations. In
this talk, I would like to discuss my ongoing work on the twisted endoscopic character
relation for Kaletha’s supercuspidal L-packets. The strategy is to imitate Kaletha’s proofof the standard endoscopic character relation in the setting of twisted endoscopy. Thus
ﬁrst I am going to review Kaletha’s construction of supercuspidal L-packets and his proofof the standard endoscopic character relation. Then I will explain a few key points inthe twisting process with an emphasis on Waldspurger’s philosophy ”l’endoscopie torduen’est pas si tordue”.
11:30 – 12:30 Ken-ichi Yoshikawa (Kyoto University)
Quasi-pullback of certain Siegel modular forms and Borcherds products.
Abstract: A holomorphic torsion invariant of K3 surfaces with involution was introduced
by myself, and it has been proved by S. Ma and me that this invariant is expressed as theproduct of an explicit Borcherds product and an explicit Siegel modular form. In thistalk, I will report that these automorphic forms are closed under the operation called thequasi-pullback. As a result, we obtain some Borcherds products as the quasi-pullbackof (the pullback via the Torelli map of) the Siegel modular form deﬁned as the productof all even theta constants.