Titles and Abstracts
Pacific Rim Complex and Symplectic Geometry Conference, Kyoto, 2022

Kento Fujita (Osaka University)
Title: The Calabi problem for Fano threefolds
Abstract: There are 105 irreducible families of smooth Fano threefolds, which have beenclassified by Iskovskikh, Mori and Mukai. For each family, we determine whether its general
member admits a Kaehler-Einstein metric or not. This is a joint work with Carolina
Araujo, Ana-Maria Castravet, Ivan Cheltsov, Anne-Sophie Kaloghiros, Jesus MartinezGarcia, Constantin Shramov, Hendrik Suess and Nivedita Viswanathan.
Yohsuke Imagi (Shanghai Tech University)
Title: Calabi–Yau Metrics on Nodal 3-folds
Abstract: I will discuss Calabi–Yau (Ricci-flat Kahler) metrics on compact nodal Calabi–
Yau 3-folds (with ordinary double points at worst). In many cases it is known alreadythat the metrics exist with suitable asymptotic decay conditions at the nodes. The glueing
constructions are also done for smoothings. But projective small resolutions are not yet
dealt with in the literature and I have a proof that I can do the glueing constructions
for them. This is of interest in itself and useful for finding special Lagrangians in theresolved Calabi–Yaus. In the talk either I’ll be speaking in detail about the metrics or I’ll
be including special Lagrangians with respect to them.
Takahiro Inayama (Tokyo University of Science)
Title: Singular Demailly-Skoda type theorem
Abstract: Demailly-Skoda’s theorem and its generalization due to Berndtsson and LiuSun-Yang assert that if a holomorphic vector bundle is Griﬃths positive, the tensor productof the symmetric power of the vector bundle and its determinant line bundle is Nakanopositive. In this talk, I explain the generalization of the Demailly-Skoda type results to a
singular Hermitian vector bundle. I also show its application.
Eunjeong Lee (Chungbuk National University)
Title : Foldings in studying flag manifolds
Abstract: Flag varieties are smooth projective varieties that provide an interesting bridge
between geometry and representation theory. For instance, a semisimple algebraic groupG, its Borel subgroup B, and a regular dominant integral weight λ, the irreducible representation with highest weight λ can always be expressed as the set of holomorphic sectionsof a certain line bundle over the flag variety G/B. A string polytope is a rational convex
1polytope that sits in the middle of this bridge. The lattice points in a string polytope
parametrize a highest weight crystal basis; it also inherits geometric information of a flagvariety such as toric degenerations, Newton–Okounkov bodies, Schubert calculus, and soon. In this talk, we study properties of string polytopes in types B and C by providing anexplicit description in these types which is analogous to Gleizer–Postnikov’s description ofstring polytopes in type A using the foldings appearing in representation theory. Moreover, we characterize string polytopes in type C which are unimodularly equivalent to theGelfand–Tsetlin polytope in type C for a specific weight. This talk is based on joint workwith Yunhyung Cho and Naoki Fujita.
Lucas Kaufmann (IBS Center for Complex Geometry)
Title: Residue currents for holomorphic foliations
Abstract: Given a holomorphic foliation F on a complex manifold, the celebrated BaumBott Theorem associates to each component of the singular set of F a residual cohomology
class whose sum satisfy an index theorem. When F is of rank one and has isolated singularities, such Baum-Bott classes can be eﬀectively computed using Grothendieck residues.
In the general case, however, no general result is known. In this talk I will show that,for general F, each Baum-Bott class can be naturally represented by a singular currentof residue type supported by the singular set. This is a joint work in progress with R.
Lärkäng and E. Wulcan.
Dano Kim (Seoul National Univerrsity)
Title: Canonical bundle formula and degenerating families of volume forms
Abstract: Canonical bundle formula and degenerating families of volume forms Abstract:
We will talk about a metric version of Kawamata’s canonical bundle formula for log CalabiYau fibrations, which says that the L2 metric carries singularity given by the discriminantdivisor and the moduli part line bundle admits a singular hermitian metric with vanishing
Lelong numbers. Applications to semipositivity theorems and to L2 extension theorems
will be discussed.
Yoosik Kim (Pusan National University)
Title: Disk potential functions of polygon spaces
Abstract: A polygon space is the moduli space of polygons in the Euclidean space with afixed length, which appears in various branches of mathematics. In this talk, we will discuss
the moduli space of polygons in the 3-dimensional Euclidean space from the perspectiveof Lagrangian Floer theory. In particular, I will talk about Fukaya-Oh-Ohta-Ono’s disk
potential function of bending torus fiber in smooth and monotone 3D polygon spaces. Thisis based on joint work with Siu-Cheong Lau and Xiao Zheng.
Toshihiro Nose (Fukuoka Institute of Technology)
Title: Meromorphic continuation and non-polar singularities of local zeta functions insome smooth cases
Abstract: It is known that local zeta functions associated with real analytic functions can2

be analytically continued as meromorphic functions to the whole complex plane. However,
the above phenomena do not occur in smooth cases generally. In this talk, the cases of somemodel of smooth functions are treated. In particular, we give the optimality of the lower
estimates of a certain quantity concerning with meromorphic continuation of local zetafunctions in the smooth model cases. To show the optimality, we investigate asymptotic
behavior of local zeta functions associated with certain smooth functions which are notreal analytic. In the cases, local zeta functions have singularities diﬀerent from poles.
Jiayin Pan (University of California, Santa Cruz)
Title: Some examples of open manifolds with positive Ricci curvature
Abstract: We give some examples of open manifolds with positive Ricci curvature. These
examples give negative answers to two open problems. One is about the properness of theBusemann function at some point, and the other one regards the singular set of Ricci limit
spaces. This is joint work with Guofang Wei.
Fumihiko Sanda (Gakushuin University)
Title: Mirror symmetry of Fano manifolds via toric degenerations
Abstract: Let X be a Fano manifold and L be a monotone Lagrangian in X. Then (achart of) a Landau-Ginzburg mirror of X is a Laurent polynomial f which is computed bycounting holomorphic disks bounded by L. Suppose that X admits a toric degeneration
to a normal toric Fano variety X ′ . In this talk, I will explain that the Newton polytope off is equal to the fan polytope of X ′ .
Weimin Sheng (Zhejiang University)
Title: Positive mass theorem with low-regularity Riemannian metrics
Abstract: In this talk, I would like to introduce our recent results with W. Jiang andH. Zhang on positive mass theorem and scalar curvature lower bounds with low-regularity
Riemannian metrics. We first consider asymptotically flat Riemannian manifolds endowedwith a continuous metric and the metric is smooth away from a compact subset withcertain conditions. I will show the positive mass theorem is true if the metric is Lipschitz
and the scalar curvature is nonnegative away from a closed subset with (n − 1)-dimensional
Hausdorﬀ measure zero. On compact manifolds with a continuous initial metric, I willshow the scalar curvature lower bound is preserved along the Ricci flow if the initial metrichas a scalar curvature lower bound in distributional sense. As an application, we use thisresult to study the relation between Yamabe invariant and Ricci flat metrics.
Yoshihiro Sugimoto (Tokyo Metropolitan University)
Title: On the number of periodic orbits in Hamiltonian dynamics
Abstract: The number of periodic orbits and fixed points of Hamiltonian diﬀeomorphisms
is one of the most important problems in symplectic topology. In this talk, I will talk about
the problem of the existence of infinitely many periodic orbits for Hamiltonian diﬀeomorphisms. Hamiltonian diﬀeomorphisms tend to have infinitely many periodic orbits.

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Yuya Takeuchi (University of Tsukuba)
Title: I’-curvatures and the Hirachi conjecture
Abstract: The Deser-Schwimmer conjecture deals with conformally invariant integrals ofRiemannian scalars, which was proved by Alexakis. Hirachi posed a CR analogue of thisconjecture, called the Hirachi conjecture. In this talk, we introduce the I’-curvatures andprove that these produce counterexamples to the Hirachi conjecture. This talk is based on
joint work with Jeﬀrey S. Case.
Yuuji Tanaka (Kyoto University)
Title: On a blowup formula for sheaf-theoretic virtual enumerative invariants on projective surfaces
Abstract: To consider a blowup formula in the theory of Donaldson’s polynomial invariants has a big advantage not only in calculating more examples or widening the accesible
range of the invariants, but also in revealing intriguing structures in the theory, such as
the modular expression of the wall-crossing terms by Goettsche and Goettsche-NakajimaYoshioka, and the fascinating structure theorem for the generating series of Donaldson
invariants by Kronheimer-Mrowka and Fintushel-Stern, since a blowup formula provides
an alternative way of computing the invariants.
On the other hand, there has been a number of exciting progress and prosperity instudies on virtual enumerative invariants, i.e., analogues of the Donaldson invariants in
Algebraic Geometry and Representation theory, such as Gromov-Witten invariants e.g. on
projective varieties, Donaldson-Thomas ones on Calabi-Yau threefolds, Mochizuki’s virtual
Donaldson invariants, and Vafa-Witten invariants on projective surfaces, etc., where one
can use virtual techniques founded by Behrend-Fantechi, Li-Tian and others to define thesedeformation invariants out of the moduli problems.
We establish a blowup formula for sheaf-theoretic virtual enumerative invariants on
projective surfaces, including Mochizuki’s ones, virtual Euler characterisctics and chiygenera, which are thought of as the instanton part and a refinement of that of the VafaWitten invariants, and other interesting generalisations of the Donaldson invariants suchas virtual Segre and Verlinde numbers, of the moduli spaces of (semi)stable sheaves on
projective surfaces.
We use Nakajima-Yoshioka’s m-stable sheaves on a projective surface, which nicelyinterpolates the moduli spaces of (semi)stable sheaves on the blowup and the original one,but with perfect obstruction theories. Our blowup formula turns out to be universal, so,e.g. we obtain a blowup formula for the generating series of the virtual chiy genera and theEuler characteristics of the moduli spaces by studying them in the case for framed sheaves
on the projective plane.
This talk is based on joint work arXiv:2107.08155 with Nikolas Kuhn and arXiv:2205.12953
with Nikolas Kuhn and Oliver Leigh.

4Jun Zhang (University of Science and Technology of China, IGP)
Title: Triangulated persistence category in symplectic geometry
Abstract: In this talk, we will introduce a new algebraic structure called triangulated
persistence category (TPC). A TPC combines the persistence module structure (fromtopological data analysis) and the classical triangulated structure so that a meaningfulmeasurement, via cone decomposition, can be defined on the set of objects. Moreover, aTPC structure allows us to define non-trivial pseudo-metrics on its Grothendieck group.
Finally, we will illustrate several unexpected properties of a TPC via its supporting example in symplectic geometry, the derived Fukaya category. In particular, we can distinguishobjects in a derived Fukaya category from a quantitative perspective.
Yang Zhou (Fudan University)
Title: K-theoretic quasimap wall-crossing and applications
Abstract: The K-theoretic Gromov-Witten invariants virtually count holomorphic curves
in smooth projective manifolds or orbifolds, using K-theory as an intersection theory. They
are interesting due to their connections to 3d gauge theories and representation theory.
For a large class of GIT quotients, the quasimap invariants are analogous to the GromovWitten invariants, defined using the moduli of epsilon-stable quasimaps as an alternative
compactification of the space of holomorphic maps from smooth domain curves. As epsilonvaries, there is a wall-crossing phenomenon, and recovering the Gromov-Witten theory as
epsilon tends to infinity.
In this talk, I will talk about the quasimap wall-crossing of K-theoretic Gromov-Witten
invariants and its applications. It is similar to the quasimap wall-crossing for cohomologicalGromov-Witten invariants, but the permutation-equivariant structure and some orbifold
subtleties lead to interesting new phenomena for the K-theoretic invariants.
This is a joint work with Ming Zhang.

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