Persistent homology and GLMY-homology

Prerequisite

The elementary theory about algebraic topology

Abstract

In applied mathematics, topological based data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. In this course we will concentrate mainly on two such techniques: persistent homology and GLMY-homology. Persistent homology is an algebraic tool for measuring topological features of shapes and functions. It casts the multi-scale organization of data into a topological formalism. In our lectures we will give some exposition of mathematical theory and show some applications in biology. Prof Yau and his collaborators introduced the new topology theory (GLMY theory) of digraph in 2012,this theory takes more abstract graph structured data as the research target,developed GLMY homology, hypergraph homology，etc. The relevant theory of this homology has been very rich, and its application has achieved good results in many fields.This course mainly sorts out GLMY homology to help students become familiar with and master the theory.

Lecturer Intro.

Assistant Reserch fellow Jingyan Li received a PhD degree from the Department of Mathematics of Hebei Normal University in 2007. Before joining BIMSA in September 2021, she has taught in the Department of Mathematics and Physics of Shijiazhuang Railway University and the School of Mathematical Sciences of Hebei Normal University as an associate professor. Her research interests include topology data analysis and simplicial homology and homotopy. Prof. Sergei Ivanov is a mathematician from St. Petersburg, Russia. His research interests include homological algebra, algebraic topology, group theory, simplicial homotopy theory, simplicial groups.