西南交通大学几何拓扑与数学物理讨论班（非正式的）

Upcoming

报告时间：2023年12月22日上午10点-11点

报告地点：西南交通大学犀浦校区X30405

报告人：周家足（西南大学）

报告题目：Recent Advances in Integral and Convex Geometry

报告摘要：The isoperimetric problem, equivalent to the isoperimetric inequality, was known in Ancient Greece. The natural extensions of the isoperimetric inequalities are Alexandrov-Fenchel inequalities. We will address the recent advances and applications in integral and convex geometry. The talk may cover some joint works with N. Fang, X. Li, C. Shi, H. Wang, W. Xu, C. Zeng, Z. Zhang and B. Zhu.

个人简介：周家足是西南大学数学与统计学院教授，数学研究所所长;中国数学会第11届常务理事；香港求是杰出青年学者奖、中国政府友谊奖、重庆市国际科技合作奖、重庆市友谊奖；湖北省楚天学者主讲教授；中华人民共和国成立60周年（2009）、70周年（2019）庆典嘉宾；论文发表在Trans. AMS 、Adv. Math. 、Adv. Appl. Math. 、Sci. China Math.、China Ann. Math. 等期刊上；主持国家自然科学基金及教育部重点基金8项。

报告时间：2023年12月12日上午10点-11点

报告地点：西南交通大学犀浦校区X30405

报告人：邹浩（北京雁栖湖应用数学研究院）

报告题目：Quantum cohomology and quantum K ring from GLSM

报告摘要： Gauged linear sigma models (GLSMs) have vast applications in the interdisciplinary area between physics and mathematics. In this talk, I will address one application of such models in quantum geometry. I will start with a short introduction of GLSMs, and then I will present how to obtain quantum cohomology and quantum K ring relations from GLSMs in concrete examples. In particular, I will introduce a Whitney-type representation for quantum K ring inspired from Coulomb branch computation in the gauge theory. 

个人介绍：邹浩，北京雁栖湖应用数学研究院和清华大学丘成桐数学科学中心博士后。2016年毕业于中国科学院大学，2021年毕业于弗吉尼亚理工大学并获得博士学位，之后便开始从事博士后研究，研究兴趣主要是规范量子场论及相关交叉领域，包括量子可积系统和数学物理等。目前在JHEP，PRD，SciPost Physics等期刊上发表SCI论文10余篇。

注记：12月11日邹浩在物理学院有另外一场学术报告【创源大讲堂】贝特/规范对应关系及其应用-西南交通大学新闻网 (swjtu.edu.cn) 感兴趣的朋友或同学可以去听听。

报告时间：2023年12月1日下午3点-4点

报告地点：西南交通大学犀浦校区X30405

报告人：李世豪（四川大学）

报告题目：我眼中的Toda方程

报告摘要：Toda方程作为一类重要的孤子方程，在1967年被提出之后就得到了广泛的研究。这个报告将讲述我眼中Toda方程研究的历史，以及在每个分支上它对应的推广。

报告人简介：李世豪，四川大学数学学院特聘研究员，研究方向是可积系统和随机矩阵，在国际知名数学物理杂志Comm. Math. Phys.，Adv. Math.，Trans. AMS等发表论文数篇，现主持国家自然科学基金青年项目和面上项目，入选四川天府峨眉计划。

报告时间：2023年12月1日下午4点-5点

报告地点：西南交通大学犀浦校区X30405

报告人：熊仪睿（四川大学）

报告题目：What is a Bridgeland stability condition and how can I construct one?

报告摘要：Stability serves as a fundamental concept in constructing moduli spaces of sheaves on varieties or modules over algebras. While classical stability conditions were well-defined for abelian categories, extending these definitions to derived categories had been an unresolved challenge. Inspired by physicists’work on string theory, T. Bridgeland proposed a satisfactory definition of stability conditions for derived categories in the early 2000s.

In this talk, I aim to provide an overview of stability conditions, starting with classical stability and then Bridgeland stability conditions. I hope to show you why the space of Bridgeland stability conditions is an interesting space-a complex manifold-by looking at the baby examples. If time permits, I will talk about my recent work on the stability conditions on local F_0.

报告人简介：熊仪睿博士毕业于英国谢菲尔德大学（导师为Tom Bridgeland），目前在四川大学访问。

报告时间：2023年12月1日下午5点-6点

报告地点：西南交通大学犀浦校区X30405

报告人：赫海龙（暨南大学）

报告题目：一个实验引发的研究

报告摘要：本报告我们从一个著名物理实验讲起，进而介绍相关的数学研究进展。

报告人简介：赫海龙为暨南大学教授，博士毕业于南京大学数学系，后在南开大学陈省身数学研究所和南京大学数学所做博士后，曾在南京师范大学工作过，研究方向为动力系统和辛几何。

报告时间：2023年11月16日上午10点到11点

腾讯会议：806-381-341

Speaker：Xiaolong Han（Tsinghua university)

Title: The geometry of the Thurston norm, geodesic laminations and Lipschitz maps

Abstract: For closed hyperbolic 3-manifolds, Brock and Dunfield made a conjecture about the upper bound on the ratio of L2-norm to Thurston norm. We first talk about its proof and describe some generic behavior. We then talk about the connection between the Thurston norm, best Lipschitz circle-valued maps, and maximal stretch laminations, building on the recent work of Daskalopoulos and Uhlenbeck, and Farre, Landesberg, and Minsky. 

报告人简介：韩肖垄，清华大学博士后，伊利诺伊大学香槟分校博士，主要研究兴趣为双曲几何，低维流形等。

 

报告时间：2023年11月17号下午3点-4点

报告地点：西南交通大学犀浦校区X30405

Speaker：Raphael Ponge（Sichuan University）

Title: Noncommutative geometry and semiclassical analysis

Abstract: Semiclassical analysis and noncommutative geometry are distinct fields within the wider area of quantum theory. Bridges between them have been emerging recently. This lays down on operator ideal techniques that are used in both fields. In this talk we shall present semiclassical Weyl’s laws for Schrödinger operators on noncommutative manifolds (i.e., spectral triples). This shows that well known semiclassical Weyl’s laws in the commutative setting ultimately holds in a purely noncommutative setting. This extends and simplifies previous work of McDonald-Sukochev-Zanin. In particular, this allows us to get semiclassical Weyl’s laws on noncommutative tori of any dimension $n\geq 2$, which were only accessible in dimension $n\geq 3$ by the MSZ approach. There are numerous other examples as well. The approach relies on spectral asymptotics for some weak Schatten class operators.

报告人简介：Raphael Ponge is a professor in Sichuan University. His research interest is noncommutative geometry.

2023年现代几何物理前沿论坛

Schedule (2023年7月18日)

时间	Speaker	Title
10:00-11:00	Andre Leclair(Cornell)	Riemann Hypothesis for physicists
	Lunch time
14:30-15:30	Weiqiang He（Sun Yat-sen）	Equivariant Hikita conjecture for minimal nilpotent orbit
15:40-16:40	Yaoxiong Wen(KIAS)	Mirror Symmetry for nilpotent orbit closures
16：50-17:50	Yi Wang(Stony Brook)	Stringy topology and Lagrangian submanifolds

地点（Place）: 西南交通大学犀浦校区综合楼403

报告题目及摘要

Speaker：Andre Leclair(Cornell University)

Title：The Riemann Hypothesis for Physicists

Abstract：The Riemann Hypothesis is widely considered as the most important unsolved problem in mathematics.  It has remained unsolved for over 150 years. In this colloquium I will describe two promising approaches to the problem based on ideas from physics, in particular the universal properties of brownian motion or random walks.   

 

Speaker：Weiqiang He(Sun Yat-sen University)

Title：Equivariant Hikita conjecture for minimal nilpotent orbit

Abstract:The theory of symplectic duality is a kind of mirror symmetry in mathematical physics. Suppose two (possibly singular)manifolds are symplectic dual to each other, then there are some highly nontrivial identities between the geometry and topology of them. One of them is the equivariant Hikita conjecture. Suppose we are given a pair of symplectic dual conical symplectic singularities, then Hikita conjecture is a relation of the quantized coordinate ring of one conical symplectic singularity to the equivariantcohomology ring of the symplectic resolution of the other dual conical symplectic singularity. In this talk, I will focus on this case: the minimalnilpotent orbit and the slodowy slice of the subregular orbit. This is a joint work with Xiaojun Chen and Sirui Yu.

Speaker：Yaoxiong Wen(KIAS)

Title：Mirror symmetry for nilpotent orbit closure

Abstract：Inspired by the work of Gukov-Witten, we investigate stringy E-polynomials of nilpotent orbit closures of type $B_n$ and $C_n$.Classically,there is a famous Springer duality between special orbits. Therefore,it is natural to speculate that the mirror symmetry we seek may coincide with Springer duality in the context of special orbits. Unfortunately, sucha naive statement fails. To remedy the situation, we propose a conjecture which asserts the mirror symmetry for certain parabolic/induced covers of special orbits. Then, we prove the conjecture for Richardson orbits and obtain certain partial results in general.  In the mirror symmetry, we find an interesting seesaw phenomenon where Lusztig's canonical quotient group plays an important role. Thistalk is based on the joint work with Baohua Fu and Yongbin Ruan, https://arxiv.org/abs/2207.10533.

 

报告人：王怡（纽约州立大学石溪分校）

题目：弦拓扑和拉格朗日子流形

摘要：Chas和Sullivan在1999年发现，流形上环路的不同相交方式可以诱导出自由环路空间（free loop space）的同调群上丰富的代数结构，由此开拓出了弦拓扑（string topology）这一领域。Fukaya及其合作者在2000年左右研究了一般情形下辛流形中拉格朗日子流形（Lagrangian submanifold）相交的Floer理论，特别地，每个拉格朗日子流形都给出了一个A-无穷代数，其中蕴含了边界落在该子流形上的伪全纯圆盘（pseudo-holomorphic disk）映射的信息。在今天的报告中，基于Fukaya、Irie和我自己的工作，我将阐释两者的联系。我将从Gromov证明C^n中不存在第一贝蒂数为零的紧致无边拉格朗日子流形讲起。

Past talks:

报告时间：2021年12月19日上午8点40分-9点10分

报告人：赵鹏（中国科学院理论物理研究所）

腾讯会议ID：721544232

报告题目：Cluster代数在数学物理中的应用

注记： 这是2021年数学学院博士论坛系列活动中的一个报告。 

报告时间：2021年12月22日（星期三） 15:00

报告人：Dr. Kento Osuga（University of Warsaw）

地址: Zoom ID: 815 1913 8183 Passcode: 039782

报告题目(Title)：Picard-Fuchs System and Five-dimensional Gauge Theory

报告摘要(Abstract)：In this talk, I will propose an effective technique to compute the prepotential of five-dimensional supersymmetric gauge theory. Explicitly, for simply-laced groups, I provide a clear construction of the Picard-Fuchs system in terms of the associated Frobenius manifold whose solutions satisfy the Seiberg-Witten special geometry relation. For non simply-laced cases, we show that an algebraic structure still exists and discuss somewhat unexpected discrepancies between the gauge theory and the Toda system. This is based on arXiv: 2110.11638 joint with Andrea Brini.

Time：3pm (UTC+8), 5 May, 2022

Speaker: Arpan Saha (ICMAT)

Zoom ID: 849 4415 5281  Passcode: 20220505

Title: The GW/DT correspondence, resurgence, and geometry

Abstract: Gromov–Witten and Donaldson–Thomas invariants are enumerative invariants that can be defined for a Calabi–Yau threefold X. Whereas the GW invariants count stable holomorphic maps from a complex curve into X, the DT invariants count coherent sheaves supported on a holomorphic curve in X subject to some stability condition. Although superficially different, it has been conjectured by Maulik–Nekrasov–Okounkov–Pandharipande that the two sets of invariants contain the same information. In this talk, we shall be exploring a realisation of this conjectural equivalence inspired by topological string theory wherein the DT invariants appear as Stokes data associated to Borel resummations of the generating function of the GW invariants, at least in the case where X is the resolved conifold. In particular, we will find in this case that all the Borel resummations are transformations of the triple sine function studied in a recent work of Bridgeland. Finally, if there is time, we will be seeing how the ambiguity from Borel resummations has a natural geometric interpretation in context of the c-map construction in supergravity. All of this is based on the arXiv preprints 2109.06878 with Murad Alim, Jörg Teschner, and Iván Tulli; 2106.11976 with Murad Alim and Iván Tulli; and 2103.05060 with Mauro Mantegazza (published in Geometriae Dedicata).

蔻享学术直播：https://www.koushare.com/lives/room/498235

百度云盘链接：https://pan.baidu.com/s/1VR4pMeXgJdvtjd_wWdu7eA 
提取码：ufm9 （有效期30天）

Dropbox链接：https://www.dropbox.com/s/60idm6kc46ia6ia/Seminar-by-Arpan-Saha.mp4?dl=0

Time：2pm (UTC+8), 9 May, 2022

Speaker: Todor Milanov(IPMU, University of Tokyo)

Zoom ID：82366360651 Passcode：20220509

Title: Fano orbifold lines of type D and integrable hierarchies

Abstract: This is a joint work with Jipeng Cheng (arXiv: 1910.03150 and 1910.12735). I am planning to divide the talk into 3 parts. First, I would like to explain a general method for constructing Hirota quadratic equations (HQEs) for semi-simple Frobenius manifolds. In the second part, I will explain how the method works in the case of quantum cohomology of a Fano orbifold line of type D. Finally, I would like to explain how to construct an integrable hierarchy from the HQEs.

蔻享学术直播：https://www.koushare.com/lives/room/366090

Time：2pm (Beijing time）, 16 May, 2022

Speaker: Andrea Brini（University of Sheffield）

Zoom ID：89341274807   Passcode: 20220516

Title: Topological strings and the relativistic Toda chain

Abstract: I will give an overview of the relation between topological strings on certain local Calabi-Yau singularities and a relativistic analogue of the root-theoretic generalisation of the periodic Toda chain. I will also point out how this fits into a web of dualities linking Chern-Simons theory on spherical space forms, five-dimensional Seiberg-Witten theory, and certain Frobenius manifolds.

Dropbox链接：

https://www.dropbox.com/s/6fyrarjm02wv3i5/Seminar-by-Andrea-Brini.mp4?dl=0

Time：4pm (Beijing time), 13 June, 2022

Speaker: Marco Fazzi (INFN)

Zoom ID：87875871625 Passcode: 20220613

Title: Geometric engineering on flops of length two

Abstract: Type IIA on the conifold is a prototype example for engineering QED with one charged hypermultiplet. The geometry admits a flop of length one. In this talk I will introduce the next generation of geometric engineering on singular geometries, namely flops of length two such as Laufer's example. Type IIA on the latter geometry gives QED with higher-charge states. In type IIB, even a single D3 probe gives rise to a nonabelian quiver gauge theory. I will show how to study this class of geometries explicitly by leveraging their quiver description, how to parametrize the exceptional curve, how to see the flop transition, and how to find the noncompact divisors intersecting the curve. With a view towards F-theory applications, I will also show how these divisors contribute to the enhancement of the Mordell-Weil group of the local elliptic fibration defined by Laufer's example.

2022 Miniworkshop on interaction between geometric topology and mathematical physics

Place: Online. The tencent meeting id is 467771970(No password). 

Remark: Tencent meeting is 腾讯会议 in Chinese. The international version of tencent meeting is voov meeting. They share the same meeting id.

Koushare live broadcast link: https://www.koushare.com/lives/room/345704

Recorded videos:  https://www.dropbox.com/s/ywsih3ztq9o6lmo/Miniworkshop%20on%20interaction%20between%20Geometric%20Topology%20and%20Mathematical%20Physics.mp4?dl=0

Schedule

Time: 9am (Beijing time), 26 May, 2022

Speaker: Dr. Peng Zhao (ITP)

Title: Remarks on 2d unframed quiver gauge theories

Abstract: 2d quiver gauge theories provide Kahler quotient construction of quiver varieties. By studying Seiberg-like dualities, we found a cluster algebra structure on the kahler moduli space. Mathematically, this translates to the equivalence of Gromov-Witten theories of quiver varieties related by cluster transformations, known as the Mutation conjecture. I will discuss examples of unframed quivers such as the kronecker quiver and the Markov quiver. They provide an infinite class of equivariant GIT quotients. Our physical analysis suggests a correspondence between the abelian necklace quiver and the nonabelian 2d SQCD.

SWJTU workshop.pdf

Time: 10:30am (Beijing time), 26 May, 2022

Speaker: Dr. Yuhang Chen (OSU)

Title: Equivariant Moduli of Sheaves on K3 Surfaces

Abstract: We study the Hirzebruch-Riemann-Roch (HRR) theorem for proper smooth

quotient Deligne-Mumford stacks, explore its relation with representation theory of nite

groups, and derive a new orbifold HRR formula via an orbifold Mukai pairing. As a rst

application, we use this formula to compute the dimensions of G-equivariant moduli spaces of stable sheaves on a K3 surface X under the action of a nite subgroup G of its symplectic automorphism group. We then apply the orbifold HRR formula to reproduce the number of xed points on X when G is cyclic without using the Lefschetz xed point formula. We prove that under some mild conditions, equivariant moduli spaces of stable sheaves on X are irreducible symplectic manifolds deformation equivalent to Hilbert schemes of points on X via a connection between Gieseker and Bridgeland moduli spaces, as well as the derived McKay correspondence. As a corollary, these moduli spaces are also deformation equivalent to G-equivaraint Hilbert schemes of points on X.

Brief_Talk_on_EMT_05252022.pdf

Lunch time

Time: 12:30pm (Beijing time), 26 May, 2022

Speaker: Fenglong You (Oslo)

Title: Relative quantum cohomology under birational transformations

Abstract:  I will talk about how relative quantum cohomology, defined by Tseng-You and Fan-Wu-You, varies under birational transformations. Relation with FJRW theory and extremal transitions of absolute Gromov--Witten theory will also be discussed.

SWJTU_Workshop_Fenglong You.pdf

Time: 2 pm(Beijing time), 26 May, 2022

Speaker: Jeongseok Oh(Imperial College London)

Title: Virtual cycles on projective completions

Abstract: For a compact quasi-smooth derived scheme M with (-1)-shifted cotangent bundle N, there are at least two ways to localise the virtual cycle of N to M via torus and cosection localisations, introduced by Jiang-Thomas. We produce virtual cycles on both the projective completion and projectivisation of N and show the ones on the former push down to Jiang-Thomas cycles and the one on the latter computes the difference. Using the idea we study the difference between quintic and twisted quintic Gromov-Witten invariants.

Chengdu_Oh.pdf

报告题目：SYZ conjecture and non-archimedean geometry

报告时间：2023年5月31日上午10：00—11：00

报告地点：西南交通大学犀浦校区X2218

报告人：袁航（Northwestern University）

摘要：Strominger-Yau-Zaslow (SYZ) 猜想，被提出作为 Calabi-Yau 流形镜像对称的几何机制，长期以来在定义对偶环面纤维化和理解奇异纤维方面存在显著的挑战。本次讲座从回顾可积系统的基础知识开始，包括symplectic和non-archimedean背景下的情况，并如何通过结合量子修正信息，精确描述对偶纤维化，以及如何通过研究non-archimedean拓扑来得到对偶奇异纤维。

报告人简介：袁航，博士毕业于纽约石溪大学，师从深谷贤治教授，目前在美国西北大学担任博士后职位。目前专注于研究如何在数学上精确地描述SYZ猜想，这是与弦论中的镜像对称性相关的问题。SYZ猜想由Andrew Strominger、Shing-Tung Yau和Eric Zaslow在20世纪90年代初提出，旨在解决Calabi-Yau多维流形之间的镜像对称性。该猜想提出了一种关于流形和镜像流形之间对应关系的几何理论框架。

更多内容可以参考袁航的个人主页 https://sites.math.northwestern.edu/~hyuan/

 

报告题目：Orbifold Hirzebruch-Riemann-Roch

报告时间：2023年6月21日上午09：30—10：30

报告地点：西南交通大学犀浦校区X30430

报告人：Yuhang Chen(OSU)

摘要：This talk is mainly expository with the purpose of demystifying the Riemann-Roch theorem for Deligne-Mumford (DM) stacks. In this talk, I will restrict DM stacks to quotient stacks. I will review some basic facts about the K-theory of quotient stacks and derive an orbifold Hirzebruch Riemann-Roch (HRR) formula for connected proper smooth quotient stacks. Let X be a connected separated quotient stack. I will study the inertia stack IX of X in details. In particular, we will decompose IX into connected components. Such a decomposition is essential in the constructions of the orbifold Chern character \tilde ch(E) and the orbifold Todd class \tilde td(E) of a coherent sheaf E on X when X is smooth. I will derive explicit formulas for \tilde ch(E) and \tilde td(E). I will define an orbifold Mukai pairing and derive an orbifold HRR formula for X when it is proper and smooth. I will show that the orbifold HRR formula for the classifying stack BG when G=Z/nZ recovers Parseval’s theorem for the discrete Fourier transform.

报告题目：Equivariant moduli theory on K3 surfaces

报告时间：2023年6月21日上午 11：00—12：00

报告地点：西南交通大学犀浦校区X30430

报告人：Yuhang Chen(Ohio State University)

摘要：In this talk, I will define equivatiant moduli spaces of stable sheaves on a projective scheme under an action of a finite group. Let X be a K3 surface, and let G be a finite subgroup G of the symplectic automorphism group of X. I will use the orbifold HRR formula to compute the dimensions of G-equivariant moduli spaces of stable sheaves on X under the action of the finite group G. I will then apply the orbifold HRR formula to reproduce the number of fixed points on X when G is cyclic without using the Lefschetz fixed point formula. I will prove that under some mild conditions, equivariant moduli spaces of stable sheaves on X are irreducible symplectic manifolds deformation equivalent to Hilbert schemes of points on X via a connection between Gieseker and Bridgeland moduli spaces, as well as the derived McKay correspondence. As a corollary, these moduli spaces are also deformation equivalent to G-equivariant Hilbert schemes of points on X.

报告的细节可以参考预印本https://arxiv.org/abs/2204.09824

报告人简介：陈宇航博士本科毕业于新加坡国立大学，博士毕业于俄亥俄州立大学，导师为Hsian-hua Tseng. 现任教于俄亥俄州立大学。

报告时间：2023年11月7日上午10点

报告地点：西南交通大学犀浦校区X30404

Speaker：Yinan Wang（PKU）

Title: 5d SCFTs from complete intersection singularities

Abstract: String theory provides a novel perspective to construct and classify many supersymmetric quantum field theories which are difficult to study with conventional QFT tools. In particular, putting M-theory/IIB superstring on canonical threefold singularities would result in a rich classes of 5d/4d superconformal field theories with eight supercharges. In this talk, I will present our new work on the cases of isolated complete intersection singularities (ICIS). We develop a systematic crepant resolution procedure of ICIS, from which we study the 5d Coulomb branch information. We also compare physical properties across 5d Coulomb branch and Higgs branch.