Enumerative Geometry in East Asia 2025

Contribution List

5. Remodeling Conjecture with inner branes, descendants and primaries

Bohan Fang (Peking University)

06/10/2025, 10:00

The Remodeling Conjecture proposed by Bouchard-Klemm-Mariño-Pasquetti relates all-genus open-closed Gromov-Witten invariants in a toric Calabi-Yau 3-manifold/3-orbifold to the Chekhov-Eynard-Orantin Topological Recursion (TR) invariants of its mirror curve. In this talk, I will describe the Remodeling Conjecture when 1) there are multiple Aganagic-Vafa Lagrangian branes, including inner...

6. Chiral correlations on elliptic curves and enumerative geometry

Si Li (Tsinghua University)

06/10/2025, 11:30

We explain an elliptic trace formula for correlations of chiral QFT on elliptic curves. As an application, we show how this leads to a corresponding holomorphic anomaly equation and enumerative geometry on elliptic curves.

7. Satake's good basic invariants for finite complex reflection groups

Yukiko Konishi (Tsuda University)

06/10/2025, 14:00

In 1980, Saito, Sekiguchi and Yano found ``flat generator system’’ on the orbit spaces of irreducible finite Coxeter Groups. Their construction can be understood in the framework of the almost duality of Frobenius manifolds proposed by Dubrovin.
In late 2010’, the story was extended to well-generated finite complex reflection groups by Arsie- Lorenzoni, Kato-Mano-Sekiguchi, and...

8. Quantum K-Rings of Partial Flag Varieties, the Coulomb Branch, and the Bethe Ansatz

Irit Huq-Kuruvilla (Academia Sinica)

06/10/2025, 16:00

We prove two conjectured presentations of the quantum $K$-ring of type A partial flag varieties, one coming from quantum field theory, the other coming from quantum integrable systems. Our main tool to do this is using abelianization, which also gives a purely geometric interpretation for the Bethe Ansatz equations, which appear in both conjectures.

10. Descendent transformations in Donaldson-Thomas wall-crossings

Henry Liu (Kavli IPMU)

07/10/2025, 10:00

In recent work with Nick Kuhn and Felix Thimm, we proved a Joyce-style "universal" wall-crossing formula for certain equivariant moduli problems of 3-Calabi-Yau type, including Donaldson-Thomas theory. An immediate and productive question is how tautological classes like descendents transform under such wall-crossings. I will present an explicit descendent transformation formula for the...

3. Refined Gromov-Witten invariants

Andrea Brini (University of Scheffield)

07/10/2025, 11:30

I will discuss a definition of refined curve counting invariants of Calabi-Yau threefolds with a C*-action in terms of stable maps on Calabi-Yau fivefolds. The corresponding disconnected generating function should conjecturally equate the Nekrasov-Okounkov K-theoretic membrane index under a refined version of the Gromov-Witten/Pandharipande-Thomas correspondence. I'll present several acid...

4. Mirror theorem and shift operators

Hiroshi Iritani (Kyoto University)

07/10/2025, 14:00

The genus-zero Gromov-Witten invariants of a smooth projective variety can be encoded in an infinite-dimensional Lagrangian submanifold, known as the Givental cone, within the loop space of the cohomology group. A Givental-style mirror theorem states that a certain explicit cohomology-valued hypergeometric series, called the I-function, lies in this Givental cone. In joint work with Coates,...

1. Geometric and Algebraic Constructions of Quantum Integrable Hierarchies

Zhe Wang (RIKEN)

07/10/2025, 15:30

The theory of integrable hierarchies is deeply related to the enumerative geometry, and in particular, quantum integrable hierarchies provide efficient tools to compute Gromov-Witten invariants via the symplectic field theory. In this talk, I will compare two different ways for constructing quantum integrable hierarchies. One construction is geometric and given by A. Buryak and P. Rossi by...

12. Stable envelopes for critical loci

Yalong Cao (Chinese Academy of Sciences)

08/10/2025, 10:00

In a joint work with Andrei Okounkov, Yehao Zhou and Zijun Zhou. We introduce stable envelopes in critical cohomology and K-theory for symmetric quiver varieties with potentials and related geometries.

Critical stable envelopes are compatible with dimensional reductions, specializations, Hall products, and other geometric constructions. In particular, for tripled quivers with canonical...

2. Quantum K-theory at roots of unity

Peter Koroteev (UC Berkeley)

08/10/2025, 11:30

I will describe how the quasimap approach to equivariant quantum K-theory is modified when the curve-counting parameter is sent not to unity, but to a primitive root of unity instead. In particular, this leads to the appearance of the Frobenius action on the moduli space. Upon reducing the quantum difference equation modulo primes, we arrive at the Grothendieck–Katz p-curvature and prove that...

11. Calabi-Yau four wall-crossing

Arkadij Bojko (SIMIS)

08/10/2025, 14:00

The Gross-Joyce-Tanaka conjecture proposes a universal wall-crossing formula for Calabi-Yau 4 theories. I will present recent progress towards proving an equivariant refinement of this framework, generalized to include insertions. This refinement can be formulated in terms of particular deformations of vertex algebras produced by adapting Joyce's construction. The utility of the theory is...

9. Symplectic duality and the Tutte polynomial

Michael McBreen (The Chinese University of Hong Kong)

09/10/2025, 10:00

The Tutte polynomial was introduced in the 1940s as a two-variable generalisation of the chromatic polynomial of a graph. It is the universal matroid invariant satisfying a deletion-contraction relation, and is the subject of much recent work.

I will describe a geometric realisation of the Tutte polynomial via the cohomology of a symplectic dual pair of hypertoric varieties. The same...

13. Critical stable envelopes and Yangians

Yehao Zhou (SIMIS)

09/10/2025, 11:30

Using the critical stable envelopes (see Yalong’s talk), we can construct solutions to Yang-Baxter equations with R-matrixes acting on the critical cohomologies of symmetric quiver varieties with potentials. Then, the FRT formalism gives natural (shifted) (super) Yangian action on these critical cohomologies. For example, in the case of tripled quiver with the canonical cubic potential, the...

14. KP Integrability in Topological Recursion

Alexander Alexandrov (IBS center for Geometry and Physics)

09/10/2025, 14:00

Topological recursion is a powerful tool in mathematical physics, applicable to various problems in enumerative geometry, such as intersections on moduli spaces and Hurwitz numbers. In my talk, I will discuss the KP integrability of topological recursion, which arises naturally in the context of the x-y swap relation. This integrability can be described through certain integral transforms,...

15. Br\'ezin--Gross--Witten numbers and Witten's intersection numbers: their combinatorics and uniform large genus asymptotics

Di Yang (University of Science and Tehnology)

09/10/2025, 16:00

Br\'ezin--Gross--Witten (BGW) numbers and Witten's intersection numbers are two families of rational numbers, that both have physical origins, topological meanings and backgrounds from matrix models. Their partition functions are known to be particular tau-functions of the KdV hierarchy, satisfying Virasoro constraints. In view of integrable systems, the origin of the BGW numbers and Witten's...

16. Seiberg duality conjecture in geometric level and its applications

Yingchun Zhang (Shanghai Jiao Tong University)

10/10/2025, 10:00

In the first part, I will introduce our in progress work on the Seiberg duality conjecture in geometric level. Consider a quiver with potential. It has been proved by many people that its quasimap I function is preserved under quiver mutation in some sense. In this work, we further consider the behavior of the scheme under quiver mutation, and we have proved that the scheme is also preserved...

17. Quantum Cohomology, Shift operators, and Coulomb branches

Kifung Chan (The Chinese University of Hong Kong)

10/10/2025, 11:30

Given a complex reductive group G and a G-representation N, there is an associated Coulomb branch algebra defined by Braverman–Finkelberg–Nakajima. In joint work with Chan and Lam, we show that these Coulomb branch algebras can be described as the largest subcomodules of the equivariant BM-homology of the affine Grassmannian on which certain shift operators admit non-equivariant limits. I will...

18. Topological Langlands duality for 3-manifolds via DT cohomology

Tasuki Kinjo (Kyoto University)

10/10/2025, 14:00

This talk concerns the Langlands program for 3-manifolds, initiated by Ben-Zvi–Gunningham–Jordan–Safronov. From the physical perspective, it arises as part of S-duality in 4d N=4 supersymmetric quantum field theory. One formulation of the Langlands duality conjecture for 3-manifolds involves infinite-dimensional DT cohomology, defined as the cohomology of certain perverse sheaves on the stack...

19. Microlocalization of virtual fundamental classes

Adeel Khan (Academia Sinica)

10/10/2025, 16:00

I will report on joint work in progress with Tasuki Kinjo, Hyeonjun Park, and Pavel Safronov, regarding Joyce's conjecture on a (-1)-shifted microlocalization of the virtual fundamental class. This construction subsumes not only the usual virtual fundamental class for quasi-smooth moduli spaces (read: perfect obstruction theories), but also other virtual class type constructions appearing...