Program

Time	Aug. 26 (Mon)	Aug. 27 (Tue)	Aug. 28 (Wed)	Aug. 29 (Thu)	Aug. 30 (Fri)
09:30 – 10:00	Welcome and Registration
10:00 – 10:50	Jeongseok Oh	Changzheng Li	Shuai Guo	Jianxun Hu	Bohan Fang
10:50 – 11:10	Break / Teatime
11:10 – 12:00	Jian Zhou	Alexander Aleksandrov	Hiroshi Iritani	Sukjoo Lee	Young-Hoon Kiem
12:00 – 14:00	Lunch
14:00 – 14:50	Yuan-Pin Lee	Eleny Ionel	Free Afternoon	Kai Hugtenberg	Free Discussion & Closing
14:50 – 15:10	Break / Teatime			Break / Teatime
15:10 – 15:40	Free Discussion	Free Discussion		Chongyu Wang
15:40 – 16:10				Honghuai Fang
16:10 – 18:00				Photo Session & Free Discussion
18:00 – 20:00				Banquet

Abstracts

Monday, August 26

Time	Speaker	Title & Abstract
10:00 – 10:50	Jeongseok Oh (Seoul National University)	Complex Kuranishi structures We develop a theory of complex Kuranishi structures on projective schemes. These are sufficiently rigid to be equivalent to weak perfect obstruction theories, but sufficiently flexible to admit global complex Kuranishi charts. We apply the theory to projective moduli spaces M of stable sheaves on Calabi-Yau 4-folds. Using real derived differential geometry, Borisov- Joyce produced a virtual homology cycle on M. In the prequel work we constructed an algebraic virtual cycle on M. We prove the cycles coincide in homology after inverting 2 in the coefficients. In particular, when Borisov-Joyce’s real virtual dimension is odd, their virtual cycle is torsion. This is a joint work with Richard Thomas.
11:10 – 12:00	Jian Zhou (Tsinghua University)	TBA
14:00 – 14:50	Yuan-Pin Lee (Academia Sinica and University of Utah)	Quantum K-theory. Quantum K-theory is a K-theoretic version of the (cohomological) Gromov-Witten theory. In this talk, I will present some thoughts on quantum K-theory, including some old results and some new ones.

Tuesday, August 27

Time	Speaker	Title & Abstract
10:00 – 10:50	Changzheng Li (Sun Yat-Sen University)	Mirror symmetry for certain blowup of Grassmannians. In this talk, we will discuss the Fano property of the blowup of a complex Grassmannian Gr(k, n) along a sub-Grassmannian Gr(r, m). We will study the quantum cohomology when (r, m)=(k, n-1), and will further discuss the mirror symmetry when k=2. This is based on my work in progress joint with Jianxun Hu, Huazhong Ke and Lei Song.
11:10 – 12:00	Alexander Aleksandrov (IBS Center for Geometry and Physics)	KP integrability in topological recursion through the x-y swap relation Topological recursion is a surprisingly universal mathematical physics tool, that has numerical applications in mathematics, for instance in combinatorics, enumerative geometry, and knot invariants. I will discuss a universal relation sometimes called the x-y swap relation, which plays a prominent role in the theory of topological recursion. In particular, the x-y swap relation is natural for the KP integrability and can be described by certain integral transforms, leading to the Kontsevich-like matrix models. This allows us to establish general KP integrability properties of the topological recursion differentials. This talk is based on a joint work with Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian, and Sergey Shadrin.
14:00 – 14:50	Eleny Ionel (Stanford University)	Counting embedded curves in 3-folds There are several ways of counting (pseudo)-holomorphic curves in Calabi-Yau 3-folds. Counting them as maps gives rise to the Gromov-Witten invariants. This overcounts multiple covers and gives rise to non-integer invariants due to their symmetries. But one can consider instead images of such maps (possibly with multiplicity), regarded either as subsets or as integral currents. This allowed us to prove a structure theorem for the GW invariants of symplectic 6-manifolds and the Gopakumar-Vafa conjecture. The latter states that the GW invariants of CY 3-folds are obtained, by a specific transform, from another set of invariants called BPS states which have better properties: integrality and finiteness. The integrality statement was proved earlier in joint work with Thomas Parker and the finiteness recently in joint work with Aleksander Doan and Thomas Walpuski. This talk presents some of the background and main ingredients of our proof, as well as recent progress, joint with Penka Georgieva, towards proving that a similar structure theorem holds for the real GW invariants of Calabi-Yau 3-folds with an anti-symplectic involution.

Wednesday, August 28

Time	Speaker	Title & Abstract
10:00 – 10:50	Shuai Guo (Peking University)	Virasoro constraints for cohomological field theory Abstract: Virasoro constraints are a hypothetical framework that arises in many enumerative geometry problems. In this talk, we will investigate the properties and applications of the Virasoro constraints for all genera. First, we will derive the ancestor form of the Virasoro constraints, which leads to a polynomial recursion relation. For semisimple cases, this recursion completely determines the generating series of higher genus invariants, extending Gathmann's result. Then, we will propose a generalized Virasoro conjecture for the CohFTs with non- flat units. For semisimple theories, we will prove this conjecture by using the Givental-Teleman reconstruction theorem. This talk is based on joint work with Qingsheng Zhang.
11:10 – 12:00	Hiroshi Iritani (Kyoto University)	Quantum cohomology of blowups Quantum cohomology is a deformation of the cohomology ring of a smooth projective variety defined by counting rational curves. The relationship between quantum cohomology and birational geometry has attracted much interest. In this talk, I will explain the following decomposition theorem for quantum cohomology of blowups: the quantum cohomology of the blowup of X along a smooth subvariety Z is a direct sum of the quantum cohomology of X and (codim(Z)-1) copies of the quantum cohomology of Z. The proof idea is based on a D-module version of Teleman's conjecture, which relates the quantum cohomology of a GIT quotient to the equivariant quantum cohomology of the original manifold via Fourier transformation.

Thursday, August 29

Time	Speaker	Title & Abstract
10:00 – 10:50	Jianxun Hu (Sun Yat-Sen University)	Some recent progress on Gamma conjectures Gamma conjectures, proposed by V. Golyshev, S. Galkin and H. Iritani, consists of conjecture O, Gamma conjecture I and II. Previous answers are affirmative. In this talk, I will talk about some counter-examples to conjecture O and Gamma conjecture I. This talk is based on a joint work with S. Galkin, H. Iritani, H. Ke, C. Li and Z. Su.
11:10 – 12:00	Sukjoo Lee (The University of Edinburgh)	Tropical Descent and Hodge Number Duality In this talk, I will present a tropical framework for computing Hodge-Deligne numbers of quasi-projective varieties, which we refer to as tropical descent theory. I will show that tropical descent holds for quasi-smooth toric hypersurfaces, which partially extends the work of Itenberg, Katzarkov, Mikhalkin, and Zharkov to non-smooth cases. This framework also yields significant applications in mirror symmetry: Hodge number duality holds for orbifold Clarke mirror pairs, providing a proof of a conjecture by Katzarkov, Kontsevich, and Pantev for orbifold toric complete intersections. If time permits, I will discuss several additional applications, including the functoriality in Fano mirror symmetry and Hodge number duality for singular varieties. This is joint work with Andrew Harder.
14:00 – 14:50	Kai Hugtenberg (Lancaster University)	Open Gromov-Witten invariants: Lagrangian cobordisms and the Fukaya category This talk reports on two projects. The first work (in progress), joint with Amanda Hirschi, constructs (genus 0) open Gromov-Witten invariants for any Lagrangian submanifold using a global Kuranishi chart construction. We also prove a relation between open Gromov-Witten invariants of Lagrangians related by a Lagrangian cobordism. Time permitting, I will discuss the second project, which concerns obtaining open Gromov-Witten invariants from the Fukaya category via an extension of the variation of Hodge structures associated to quantum cohomology.
15:10 – 15:40	Chongyu Wang (Peking University)	On A Tautological Relation Conjectured By Buryak-Shadrin Tautological relations on moduli spaces $\overline{\mathcal{M}}_{g,n}$ of stable curves are important topics. Recently, Buryak and Shadrin conjectured a tautological relation which has the form $B^m_{g, \textbf{d}}=0$ where $m\geq 2, n \geq 1$ and $|\textbf{d}| \geq 2g+m-1$. We proved that the conjecture holds if it is true for the $m=2$ and $|\text{\emph{d}}| = 2g+1$ case. This reduces the proof of this conjecture to checking finitely many cases for each genus $g$. In particular, we proved the conjecture for the $g=1$ case. I will explain our proof and some calculations in this report. This is a joint work with Prof. Xiaobo Liu.
15:40 – 16:10	Honghuai Fang (Peking University)	State integrals over local field and A-polynomials We focus on the generalized Teichmüller TQFT over local field constructed by Garoufalidis and Kashaev. This new TQFT with infinite-dimensional Hilbert spaces is conjecturally related to point counting of the A-polynomial curve, similar to what has been observed in the mirror symmetry of Calabi-Yau manifolds. We will show how these relevant topological invariants relate to A-polynomials of knots.

Friday, August 30

Time	Speaker	Title & Abstract
10:00 – 10:50	Bohan Fang (Peking University)	Mirror symmetric Gamma conjecture for toric Calabi-Yau 3-orbifolds I will explain the correspondence between K-theoretic framing of a toric Calabi-Yau 3-orbifold and Lagrangian cycles on the mirror curve. Under such correspondence the oscillatory integral on the mirror curve produces the expected genus zero Gromov-Witten invariants. By Givental-Teleman's graph sum expression for Gromov-Witten invariants, this further gives an all-genus descendant formula using the topological recursion.
11:10 – 12:00	Young-Hoon Kiem (Korea Institute for Advanced Study)	Gromov-Witten invariants for branched covers A fundamental idea for computing Gromov-Witten invariants is to push the computation to simpler spaces like projective spaces. When the target manifold X is a complete intersection in a projective space P, the virtual fundamental class of the moduli space M(X) of stable maps to X coincides with the cosection localized virtual fundamental class of the moduli space of stable maps to P with an additional field. Hence we can enumerate curves in X by studying certain decorated moduli spaces of curves in P. In this talk, I will extend this idea to the case where the targent manifolds are branched covers of simpler spaces. Based on a joint work with Hyeonjun Park.

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Room Type	Standard Cost*	Standard No. of People	Remark
Standard Double Room	95,000 KRW	2	Mountain View
Standard Twin Room	95,000 KRW	2	Mountain View
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Breakfast per person	19,000 KRW
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For academic inquiries, please contact:

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