2022-11-21 Mon
The $Delta$-twisted homology and fiber bundle structure of twisted simplicial sets
BIMSA Topology SeminarSpeaker: Mengmeng Zhang Hebei Normal University and BIMSA
Time: 15:30-17:00
Venue: 1129B
Zoom: 537 192 5549（PW: BIMSA）
Abstract
In this talk, I will give a brief introduction for simplicial set theory. Then I will report our recent progress for unifying $delta$-homology, introduced by Alexander Grigor'yan, Yuri Muranov and Shing-Tung Yau, and twisted Cartesian product, introduced by Barratt, Gugenheim and Moore. We introduce $\Delta$-twisted Carlsson construction of $\Delta$-groups and simplicial groups, whose abelianization gives a twisted chain complex generalizeing the $delta$-homology, called $\Delta$-twisted homology. We show that Mayer-Vietoris sequence theorem holds for $\Delta$-twisted homology. Moreover, we introduce the concept of $\Delta$-twisted Cartesian product as a generalization of the twisted Cartesian product, and explore the fiber bundle structure. The notion of $\Delta$-twisted smash product, which is a canonical quotient of $\Delta$-twisted Cartesian product, is used for determining the homotopy type of $\Delta$-twisted Carlsson construction of simplicial groups.
Organizers：Jie Wu, Nanjun Yang, Jingyan Li
2022-11-22 Tue
Categorical symmetry — applications in 1+1D
Category and Topological Order SeminarSpeaker: Arkya Chatterjee Massachusetts Institute of Technology
Time: 09:30-11:00
Venue: Online
Tencent: 607 3645 0351
Abstract
Symmetries are among the most important tools in the toolkit of a theoretical physicist. In the context of condensed matter physics, there is a long tradition of using symmetry to label and distinguish different phases of matter. The notion of symmetry becomes particularly rich in quantum systems; we now understand that symmetries come in various shapes and forms: anomaly-free, ('t Hooft) anomalous, higher-form, higher group, algebraic/non-invertible etc. All of these adjectives for symmetry may be unified, at least for finite symmetries, using the mathematical formalism of topological order in one higher dimension. We call this unified framework categorical symmetry. This categorical unification of symmetry has various applications in different contexts. In this talk, I will present two applications for 1+1D lattice models: identifying dualities and obtaining constraints on global phase diagrams. In the first part, I will discuss how the algebra of local symmetric operators encodes information about its categorical symmetry thereby leading us to dualities between different symmetry descriptions. In the second part, I will discuss how the relationship between boundary theories of 2+1D topological order helps us constrain the global phase diagram of 1+1D theories with finite symmetry. (Based on: arXiv:2203.03596 and 2205.06244)
Organizers：Hao Zheng
2022-11-22 Tue
Generalized Paley Graphs, Finite Field Hypergeometric Functions and Modular Forms
BIMSA-YMSC Tsinghua Number Theory SeminarSpeaker: Dermot McCarthy Texas Tech University
Time: 10:30-11:30
Venue: 1118
Zoom: 293 812 9202（PW: BIMSA）
Abstract
In 1955, Greenwood and Gleason proved that the two-color diagonal Ramsey number $R(4,4)$ equals 18. Key to their proof was constructing a self-complementary graph of order 17 which does not contain a complete subgraph of order four. This graph is one in the family of graphs now known as Paley graphs. In the 1980s, Evans, Pulham and Sheehan provided a simple closed formula for the number of complete subgraphs of order four of Paley graphs of prime order. Since then, \emph{generalized Paley graphs} have been introduced. In this talk, we will discuss our recent work on extending the result of Evans, Pulham and Sheahan to generalized Paley graphs, using finite field hypergeometric functions. We also examine connections between our results and both multicolor diagonal Ramsey numbers and Fourier coefficients of modular forms. This is joint work with Madeline Locus Dawsey (UT Tyler) and Mason Springfield (Texas Tech University).
Organizers：Hansheng Diao, Yueke Hu, Emmanuel Lecouturier, Cezar Lupu
2022-11-23 Wed
Geometry of quantum state spaces
Geometry and Gravitation SeminarSpeaker: Ingemar Bengtsson University of Stockholm
Time: 17:15-18:30
Venue: 1120
Zoom: 839 2831 2262（PW: BIMSA）
Abstract
Geometry of classical mechanics usually means symplectic geometry. In quantum mechanics this geometry is inseparably joined to the geometry of probability theory, creating a very rich structure. I will introduce this structure from scratch, assuming that the audience has not spent any thought on the geometry of finite dimensional quantum mechanics. But I will be gently leading up to a point of view from where you can see some unsolved problems that I am working on.
Organizers：Lars Andersson
2022-11-24 Thu
Deep adaptive sampling for numerical PDEs
BIMSA-Tsinghua Seminar on Machine Learning and Differential EquationsSpeaker: Tao Zhou AMSS, CAS
Time: 10:00-11:30
Venue: 1129B
Zoom: 537 192 5549（PW: BIMSA）
Abstract
Adaptive computation is of great importance in numerical simulations. The ideas for adaptive computations can be dated back to adaptive finite element methods in 1970s. In this talk, we shall first review some recent development for adaptive method with applications. Then, we shall propose a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. In particular, we propose the failure informed PINNs (FI-PINNs), which can adaptively refine the training set with the goal of reducing the failure probability. Compared to the neural network approximation obtained with uniformly distributed collocation points, the developed algorithms can significantly improve the accuracy, especially for low regularity and high-dimensional problems.
Speaker Intro
周涛，中国科学院数学与系统科学研究院研究员。曾于瑞士洛桑联邦理工大学从事博士后研究。主要研究方向为不确定性量化、偏微分方程数值方法以及时间并行算法等，近期的主要研究课题包括深度学习与科学计算，深度生成模型及其应用等。在国际权威期刊如SIAM Review、SINUM、JCP等发表论文70余篇。2018年获优秀青年科学基金资助，2022年获中组部高层次人才专项资助。现担任SIAM J Sci Comput、J Sci Comput等国际期刊编委，国际不确定性量化期刊（International Journal for UQ）副主编。
Organizers：Fansheng Xiong, Wuyue Yang, Wen-An Yong, Yi Zhu
2022-11-24 Thu
隐Markov链模型简介与应用
Internal Seminar on Machine Learning and Differential EquationsSpeaker: Congwei Song BIMSA
Time: 14:00-16:00
Venue: 1129B
Zoom: 537 192 5549（PW: BIMSA）
Speaker Intro
Congwei Song received the master degree in applied mathematics from the Institute of Science in Zhejiang University of Technology, and the Ph.D. degree in basic mathematics from the Department of Mathematics, Zhejiang University, worked in Zhijiang College of Zhejiang University of Technology as an assistant from 2014 to 2021, from 2021 on, worked in BIMSA as asistant researcher. His research interests include machine learning, as well as wavelet analysis and harmonic analysis.
Organizers：Wuyue Yang, Fansheng Xiong, Xiaopei Jiao
