2022-10-31
Global structures of 3d SUSY QFTs from geometry
Geometry and Physics Seminar
报告人 Yihan Wang Peking University
时 间 13:00-14:30 Mon
地 点 1110
Zoom 293 812 9202（PW: BIMSA）
摘要
Symmetry Topological Field Theory (SymTFT) is a novel tool which captures different choices of global structures of a QFT. In this work, we present the derivation of the SymTFT of 3d SUSY QFTs from an M-theory geometric perspective. For the applications, we focus on AdS4/CFT3 setups, including ABJ(M) theories and 3d N=2 toric CY4 constructions. Higher-form symmetries and mixed anomalies of these physical theories will be discussed. Reference: 2210.03703 w/ D. W. Gould, M. van Beest, S. Schafer-Nameki.
组织者：张其明、Hossein Yavartanoo
2022-10-31
On the distribution problem of Selmer groups
BIMSA Topology Seminar
报告人 朱秀武
时 间 15:30-17:00 Mon
地 点 1129B
Zoom 537 192 5549（PW: BIMSA）
摘要
The distribution problem of arithmetic objects in some particular family is interesting. In this talk, we fix a rank and discuss the densities of the ideal class groups of quadratic fields and the Selmer groups of elliptic curves in some twisted families. The idea is to interpret them as ranks of the matrices of residue symbols; then study the distribution of residue symbols.
组织者：吴杰, 杨南君, 李京艳
2022-11-01
Slopes of modular form and ghost conjecture
BIMSA-YMSC Tsinghua Number Theory Seminar
报告人 Bin Zhao Capital Normal University
时 间 16:00-17:00 Tue
地 点 1118
Zoom 293 812 9202（PW: BIMSA）
摘要
In 2016, Bergdall and Pollack raised a conjecture towards the computation of the p-adic slopes of Hecke cuspidal eigenforms whose associated p-adic Galois representations satisfy the assumption that their mod p reductions become reducible when restricted to the p-decomposition group. In this talk, I will report the joint work with Ruochuan Liu, Nha Truong and Liang Xiao to prove this conjecture under mild assumptions. I will start with the statement of this conjecture and the intuition behind it. Then I will explain some strategies of our proof. If time permits, I will mention some arithmetic applications of this conjecture.
组织者：Hansheng Diao, Yueke Hu, Emmanuel Lecouturier, Cezar Lupu
2022-11-01
Dualities and (higher) categorical symmetries in quantum lattice models
Category and Topological Order Seminar
报告人 Clement Delcamp Ghent University
时 间 21:00-22:30 Tue
地 点 1131
Zoom 886 2323 9641
摘要
Over the past few years tremendous progress has been made in our understanding of quantum theories by interpreting symmetries in terms of topological operators. This had led to a generalization of the notion symmetry whereby operators are organized into higher algebraic structures. Prime examples of theories with generalized (categorical) symmetries are obtained by gauging finite group symmetries. In this talk I will present recent progress to realize such symmetry operators together with the corresponding duality operators in quantum lattice models. The corresponding (higher) categorical charges as well as the fate of topological sectors under dualities will also be discussed.
组织者：郑浩
2022-11-02
Module categories for SU(N)_k
BIMSA-Tsinghua Quantum Symmetry Seminar
报告人 Hans Wenzl University of California at San Diego
时 间 10:30-11:30 Wed
地 点 1131
Zoom 537 192 5549（PW: BIMSA）
摘要
Module categories of a modular tensor category are characterized by a modular invariant. Some of them can be easily found using symmetries of the fusion rings, such as orbifolds and charge conjugations. However, it is not clear how to get an explicit description of the related module categories. We propose a general description of such module categories which have already been explicitly constructed in many cases via deformations of embeddings of orthogonal or symplectic groups into unitary groups. Some of these results were obtained in joint work with Edie-Michell.
组织者：刘正伟, Sebastien Palcoux, 王亦龙, 吴劲松
2022-11-02
Einstein manifolds and symmetry
BIMSA-BIT Differential Geometry Seminar
报告人 Ramiro Lafuente
时 间 16:00-17:00 Wed
地 点 Online
Zoom 559 700 6085（PW: BIMSA）
摘要
In this talk we will discuss Einstein manifolds invariant under an isometric Lie group action. Our main goal is to explain the proof of the Alekseevskii conjecture (1975) for homogeneous Einstein spaces of negative Ricci curvature, recently obtained in joint work with C. Böhm (Münster). To that end, we will also present new structure results for Einstein metrics on principal bundles. We will conclude with some open questions and future directions.
组织者：Kotaro Kawai, Sebastian Heller, Lynn Heller, Chao Qian
2022-11-03
神经网络与偏微分方程数值解
BIMSA-Tsinghua Seminar on Machine Learning and Differential Equations
报告人 蔡志强 普渡大学
时 间 10:00-11:30 Thu
地 点 1129B
Zoom 537 192 5549（PW: BIMSA）
摘要
本次报告将介绍我们最近关于神经网络的工作及其在偏微分方程数值解中的应用。报告的第一部分是使用神经网络数值求解线性和非线性标量双曲守恒律方程，这类问题的解通常具有不连续性。针对此类问题，我将展示基于神经网络的方法在自由度数量方面优于传统基于网格的方法。报告的第二部分是关于我们的自适应网络扩增(ANE)方法。开发ANE方法是为了解决一个基本、开放的问题，即如何自动设计一个最优的神经网络架构，以在规定的精度内逼近函数和偏微分方程的解。此外，针对训练产生的非凸优化问题，ANE方法提供了一个获得良好初始化的自然过程。
人物介绍
蔡教授在美国普渡大学数学系任教。他在华中科技大学获计算机科学学士学位和应用数学硕士学位，并于1990年在美国科罗拉多大学获得应用数学博士学位。1996年，他赴普渡大学任副教授，此前在布鲁克海文国家实验室和纽约大学库朗研究所任博士后研究员，并在南加州大学担任助理教授。自 2003 年以来，他一直是劳伦斯利弗莫尔国家实验室的暑期访问教授。他的研究方向是偏微分方程数值解及其在流体和固体力学中的应用。他的主要兴趣是计算机模拟的精度控制和复杂系统的自适应数值方法，最近，他专注于研究神经网络以解决具有挑战性的偏微分方程。
组织者：熊繁升, 杨武岳, 雍稳安, 朱毅
2022-11-04
Quantitative K-theory and some applications to geometry
YMSC-BIMSA Quantum Information Seminar
报告人 郭昊 Tsinghua University
时 间 09:30-10:30 Fri
地 点 清华大学近春园西楼一层报告厅
Tencent 337 8937 1456
摘要
I will try to give an accessible introduction to the ideas of quantitative K-theory for operator algebras, followed by some recent applications of this theory to differential geometry via index theory of elliptic operators. Part of this is joint work with Guoliang Yu and Zhizhang Xie.
人物介绍
Hao Guo obtained my PhD from the University of Adelaide in 2018 under Mathai Varghese and Hang Wang. Before coming to Tsinghua, he was a postdoc at Texas A&M working with Guoliang Yu. He is currently an Assistant Professor at Tsinghua University. His research is concerned with connections between operator algebras, geometry, topology, and group theory.
组织者：刘正伟
