Students Seminar on Mathematical Physics

报告人 Speaker:Jialin Chen (CSRC)
组织者 Organizer:Bo Lin, Reiko Liu
时间 Time:2024-06-07 Friday 19:30-21:00
地点 Venue:Online Tencent: 863-757-464

Upcoming Talk:

Title: 场论积分的计算方法:从平直到de Sitter
Speaker: 陈家麒 (北京计算科学研究中心)
Date: 6-7 Friday
Time: 19:30-21:00 (Beijing time)
Venue: #腾讯会议:863-757-464


微扰场论是理论物理研究中极为强力的工具,我将以分部积分方法(IBP)和基于 IBP 的微分方程方法为主轴,介绍近年来场论中积分计算理论与技术的一些发展,穿插介绍一些我过去的工作,包括正则微分方程(近十年来最强力的解析计算方法)的数学结构与 intersection theory 的关系,以及近期我们将 IBP 与微分方程方法推广到 de Sitter 时空用于计算暴胀关联的工作。


Past Talks:

Title: Tetrahedron equation, cluster algebra and supersymmetric field theories
Speaker: Xiaoyue Sun (YMSC)
Date: 5-31 Friday
Time: 19:00-20:30 (Beijing time)
Venue:   #腾讯会议:100-120-784 会议密码:402492


The tetrahedron equation, a three-dimensional analogue of the Yang-Baxter equation, is the fundamental relation in studying three-dimensional integrable systems. In this talk, I will discuss the construction of solutions of the tetrahedron equation using cluster algebra, based on work with my supervisor, Junya Yagi (arXiv:2211.10702) and further developed with Rei Inoue, Atsuo Kuniba, Yuji Terashima, and Junya Yagi (arXiv:2403.08814). Our cluster algebraic approach reproduces most known solutions of the tetrahedron equation. I will also briefly talk about how these solutions can be identified with the partition functions of certain 3d N=2 gauge theories on a squashed sphere.

Title: UV finiteness for holomorphic field theories
Speaker: Minghao Wang(Boston University)

Date: 5-24 Friday
Time: 20:00-21:30 (Beijing time)
Venue: #腾讯会议:372-440-524 会议密码:783994

Abstract: I will describes a compactification of moduli spaces of graphs with boundaries and prove UV finiteness for holomorphic field theories. The gauge anomalies are given by the integration over the boundary of the compactified moduli spaces. I will introduce some applications of this technique.
Reference: 1.

Title: Investigations on the Non-Hermitian Skin Effect

Speaker: Zixi Fang

Date: Thursday 23 November 2023

Time: 19:20-21:45 (Beijing time)

Venue: Shuangqing Complex B627


The non-Hermitian system has been extensively researched in recent years. The concept of the non-Hermitian skin effect is intriguing as it violates the Bloch theorem, causing the eigenstates of the system to differ significantly under open boundary conditions compared to periodic boundary conditions. In this presentation, I will introduce the concept of the non-Hermitian skin effect, highlighting its distinctive features such as scattering invisibility, unstable bound states, and more.

Title: Dubrovin conjecture from a GLSM viewpoint
Speaker: Jin Chen
Date: Tuesday 7 November 2023
Time: 19:20-21:45 (Beijing time)


Dubrovin conjecture establishes a relation between the Stokes data for the quantum cohomology of a Fano variety X, and the exceptional collection of the objects in the derived category of coherent sheaves on X. In this talk, I will explain how to interpolate the two objects via the hemi-sphere partition function of a GLSM with the target space of X. In this setup, the Stokes data can be interpreted as soliton numbers between different vacua in the deep infra-red, while the exceptional collection is identified as B-branes in the weakly coupled geometric phase of the theory. In addition, by introducing twisted masses, I will also show how to generalize the Dubrovin conjecture in an equivariant way.

Title: 2d-4d correspondence from the Nekrasov partition function
Speaker: Yihua Liu
Date: Tuesday 31 October 2023
Time: 19:20-21:45 (Beijing time)
Venue: Shuangqing Complex A513


In this talk I will briefly introduce the 2d-4d correspondence in terms of the Nekrasov partition function with irregular Liouville conformal blocks, and the construction of irregular correlation function from free field realizations, and another integrable system that the irregular conformal blocks satisfies.


Title: Disk partition function of 2d N=(2,2) GLSM
Speaker: Bo Lin
Date: Tuesday 24 October 2023
Time: 19:20-21:45 (Beijing time)
Venue: Shuangqing Complex A513


In this talk I’ll introduce the disk partition function of 2d N=(2,2) GLSM with boundary, together with several properties of quantum Kahler moduli space and its resolution which shall be close related to the symmetry of derived category.

Title: 2d Free Fermion Carrollian CFT Model
Speaker: Zehua Xiao
Date: Tuesday 17 October 2023
Time: 19:20-21:45 (Beijing time)
Venue: Shuangqing Complex A513


I will introduce the 2d free fermion model on the Galilean/Carrollian geometry. In this model, the modes of the Noether charges form an infinite dimensional BMS algebra. After canonical quantization, we find the fusion laws of the primary operators in NS vacuum and R vacuum in highest weight representation. All states in highest weight representation are generated by four primaries and one seed operator K. The organization of these states forms a staggered module. We also calculate the correlation functions and partition functions for the highest weight representation and the induced representation. Together with the 2d free BMS scalar model, we construct an N=2 supersymmetric Carrollian CFT model and the supercharges indeed lead to the BMS SUSY algebra. 

Title: Holography and Koszul duality
Speaker: Tianqing Zhu
Date: Tuesday 10 October 2023
Time: 19:20-21:45 (Beijing time)
Venue: Shuangqing Complex A513


I will illustrate the idea that the holography in the twisted case can be interpreted as Koszul duality in mathematics. As examples, I will show the example of the holography between N D2 branes and K D4 branes in a 6d topological string theory, which can be interpreted as the duality between the large N instanton moduli space and the gl_K spin chain.
Ref: 1809.00372, 2111.06876, 1505.06703, 1606.00365, 1705.02500, 1709,09993, 2001.02177