报告人 ：Vsevolod Chernyshev（HSE，莫斯科）

时间：2023年06月02日 17:00--

Zoom ID：343 236 0020  code：147258

摘要：Topological Data Analysis is a recent field that emerged from various works in applied algebraic topology and computational geometry during the first decade of the century. TDA started as a field with the pioneering works of Edelsbrunner et al. (2002) and Zomorodian
and Carlsson (2005) in persistent homology and was popularized in a landmark paper in 2009 Carlsson (2009). TDA is mainly motivated by the idea that topology and geometry provide a powerful approach to infer robust qualitative, and sometimes quantitative, information about the structure of data. Topological Data Analysis aims at providing well-founded mathematical, statistical and algorithmic methods to infer, analyze and exploit the complex topological and geometric structures underlying data that are often represented as point clouds in Euclidean or more general metric spaces.
What will be discussed in our course:
What is topology? Algebraic invariants. Topological processes: filtrations. Estimation of intrinsic dimension. Simplicial complexes. Clique complex. First Betti number. Betti numbers. Persistent homologies. Main Structural Theorem about persistence modules. How to make the calculations effective. Čech filtration, Vietoris–Rips filtration. How to compare filtrations and diagrams. Hodge Laplacians. Homologies and cohomologies. Hodge decomposition. Spectrum of Laplacians.

简介：Dr. Vsevolod Chernyshev is an Associate Professor at HSE University, Moscow (Russia). He obtained his Ph.D. at Lomonosov University in 2008 under the supervision of Prof. Shafarevich. He was a research visitor at University of Bristol, UK, McGill University Canada, Ruhr- Universität Bochum, Germany, Weizmann Institute, Israel, and others. He is an author of more than 30 articles on dynamical systems, number theory, mathematical physics, geometry and applications.

邀请人：鲁澧

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