# 2024 BICMR-IBSCGP

Conference on Gromov-Witten Theory and Related Topics

**August 26–30, 2024**

**Jeju Island, South Korea**

## Organizers

- Xiaobo Liu (Peking University)
- Yong-Geun Oh (IBS Center for Geometry and Physics & POSTECH)
- Gang Tian (Peking University)
- Alexander Aleksandrov (IBS Center for Geometry and Physics)

## Invited Speakers

- Alexander Aleksandrov (IBS Center for Geometry and Physics)
- Bohan Fang (Peking University)
- Honghuai Fang (Peking University)
- Shuai Guo (Peking University)
- Jianxun Hu (Sun Yat-Sen University)
- Kai Hugtenberg (Lancaster University)
- Eleny Ionel (Stanford University)
- Hiroshi Iritani (Kyoto University)
- Young-Hoon Kiem (Korea Institute for Advanced Study)
- Sukjoo Lee (The University of Edinburgh)
- Yuan-Pin Lee (Academia Sinica and University of Utah)
- Changzheng Li (Sun Yat-Sen University)
- Jeongseok Oh (Seoul National University)
- Chongyu Wang (Peking University)
- Jian Zhou (Tsinghua University)

## Venue

Azaria Hall, Uni Hotel Jeju, Jeju Island, South Korea

* For the location of the conference site, click **here** for google map.

## Registration

Online registration is not available.

Registration Period: 2024-05-20 - 2024-07-31

## 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 structuresWe 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 relationTopological 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-foldsThere 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 theoryAbstract: 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 blowupsQuantum 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 conjecturesGamma 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 DualityIn 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 categoryThis 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-ShadrinTautological 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-polynomialsWe 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-orbifoldsI 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 coversA 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. |

## Abstracts Book & Pre-arrival Guide Download

Please click here to download.

## Accommodation

We regret to say that we cannot support your travel and local expenses unless the conference promised to pay.

For booking accommodation in Uni Hotel Jeju, please fill out the form (Click **here** to download) and send it to Ms. Soonok Jung by 12:00 PM, July 26, 2024. (Email: sojung@ibs.re.kr)

If you are uncomfortable providing your private card information on the form, please leave the relevant fields blank and contact the hotel directly to provide your card details.

(Contact: Phone: +82- 064-714-5001, Email: info@unihotel.co.kr)

There is a limited number of rooms available, so please make a reservation as soon as you can.

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 |

Family Suite | 255,000 KRW | 4-5 | Ocean View |

Breakfast per person | 19,000 KRW | ||

Contact | Phone: +82- 064-714-5001, Email: info@unihotel.co.kr |

## Visa

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## Taxi Card(for Conference Venue Directions)

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## Contact

For academic inquiries, please contact:

Dr. Alexander Aleksandrov at alex@ibs.re.kr

For administrative inquiries, please contact :

Soonok Jung at sojung@ibs.re.kr