Symplectic Geometry and Mathematical Physics Seminar

Symplectic Geometry and Mathematical Physics Seminar
2024-05-29 10:30-11:30
MCM410

 Introduction:

This is a series seminar organized by MCM on Symplectic Geometry and Mathematical Physics at MCM410 on each Wednesday. If you have any questions, please feel free to contact us (mcmoffice@math.ac.cn). 


Organizers:

Yalong Cao and Zhengyi Zhou

 

Time & Venue:

Each Wednesday,  MCM410

 

Upcoming talks:

Date: May 29, 2024

Time: 10:30-11:30

Speaker: Prof. Bohan Fang (Beijing International Center for Mathematical Research)

Title: Oscillatory integrals in mirror symmetry

Abstract: I will describe the oscillatory and period integrals on the B-side of mirror symmetry. They correspond to Gromov-Witten primary and descendant invariants of Gamma-modified twisted Chern classes of the mirror coherent sheaves. The cycles for integration correspond to these mirror sheaves by homological mirror symmetry, and one may obtain higher genus invariants if using correct higher genus B-model integrands. I will explain some examples in the setting of toric mirrors and Gross-Hacking-Keel mirror LG models, and discuss application to Gamma conjectures in the toric setting.


Date: May 29, 2024 (Wednesday)

Time: 16:30-17:30

Speaker: Prof. Qizheng Yin (Beijing International Center for Mathematical Research)

Title: Cohomological and motivic aspects of compactified Jacobian fibrations

Abstract: Beauville showed using Fourier transforms that the Chow ring/motive of an abelian variety admits a natural, multiplicative decomposition. I will explain how Beauville’s theory can be extended to certain abelian fibrations with singular fibers. One notable consequence of this extension is a proof of the P=W conjecture in nonabelian Hodge theory. In this talk I will focus on aspects beyond P=W, and discuss some related open questions. Joint work in progress with Davesh Maulik and Junliang Shen.


Date: May 31, 2024 (Friday)

Time: 14:00-15:00

Speaker: Oliver Edtmair (ETH Zurich)

Title: TBC

Abstract: TBC


Date: June 5, 2024

Time: TBC

Speaker: TBC

Title: TBC

Abstract: TBC


Date: June 12, 2024

Time: 14:00-15:00

Speaker: Dr. Yu-Wei Fan (YMSC)

Title: TBC

Abstract: TBC


Date: June 19, 2024

Time: 14:00-15:00

Speaker: Dr. Honghao Gao (YMSC)

Title: TBC

Abstract: TBC


Date: June 26, 2024

Time: 14:00-15:00

Speaker: Dr. Yu Pan (Tianjin University)

Title: TBC

Abstract: TBC


Date: April 10, 2024

Time: 10:30-11:30

Speaker: Prof. Si Li (Tsinghua Univ)

Title: Holomorphic Chern-Simons at Large N 

Abstract: We describe the coupling of holomorphic Chern-Simons theory at large N with Kodaira- Spencer gravity. The 1st order deformation is realized by the Loday-Quillen-Tsygan Theorem on the Lie algebra cohomology of large N matrices. We show that the dynamics of Kodaira-Spencer gravity is fully recovered from this large N holomorphic Chern-Simons theory.


Date: May 15, 2024

Time: 10:00-11:00

Speaker: Prof. Zhengyu Zong (Tsinghua Univ)

Title: Open WDVV equations for toric Calabi-Yau 3-folds

Abstract: The Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations is an important system of equations in the study of genus zero Gromov-Witten invariants. It implies the associativity of the quantum product. The associativity of the quantum product has many important applications including the recursive formula given by Kontsevich and Manin that calculates the Gromov-Witten invariants of the projective plane. The system of open WDVV equations plays an important role in the study of open Gromov-Witten invariants. It can be viewed as an extension of the WDVV equation to the open sector. The natural structure that captures the WDVV equation is that of a Frobenius manifold. Similarly, the system of open WDVV equations determines the structure of an F-manifold, a generalization of a Frobenius manifold.  

In this talk, we prove two versions of open WDVV equations for toric Calabi-Yau 3-folds.  The first version leads to the construction of a semi-simple (formal) Frobenius manifold and the second version leads to the construction of a (formal) F-manifold. This is a joint work with Song Yu.