Topological structures of higher-order interaction networks

Title: Topological structures of higher-order interaction networks

Speaker: Wu Jie(Yanqi Lake Beijing Insititute of Mathematical Sciences and Applications)

Time: 2023-03-31, 14:00-15:00

Location: 206, Building 2, Hainayuan, School of Mathematica Sciences, Zijingang Campus

Abstract:  The structure of higher-order interactions in complex network is one of the most important scientific challenges. Complex system received 2021 Physics Nobel Prize. On the other hand, comparing with that there are a lot of well-developed mathematical tool (from graph theory) on pairwise interaction networks, there are limited mathematical tools on higher-order interaction networks so far. In this talk, guided by the applications to higher-order interaction network, we will discuss some topological approaches to graphs and hypergraphs beyond TDA, including path homology introduced by Professor Shing-Tung Yau et al, and their generalizations such as hypergraph homology, which is an extension of simplicial homology. We will also report some of our recent works on the topic, including a frame work for introducing a new theory which unifies various aspects of topological approaches for data science, by being applicable both to point cloud data and to graph datas.

Introduction of speaker: Wujie, researcher of Yanqi Lake Beijing Insititute of Mathematical Sciences and Applications, born in 1964 in Zhejiang Wenzhou, Ph.D. in Mathematics from University of Rochester, postdoctoral reasearcher at Mathematic Reaserch Institute, University of California, Berkeley, former tenured professor at National Unviersity of Singapore's Departement of Mathematics, started to work at Yanqi Lake Beijing Insititute of Mathematical Sciences and Applications in December, 2012, whose main reasearch fields include algebraic topology and applied topology. Achievements in algebraic topology theory research include establishing the fundemental relationship between homotopy and braid theory, and determining the fundamental relationship between loop space homotopy theory and permutation theory. In applied topology theory has been applied to the field of big data, and a series of results have been obtained. Publishing over 90 papers in presitigous math journal, he was awarded the Singapore National Science Award in 2007 and was supported by the National Natural Science Foundation of China's Joint Funds for OVersea Research(Distinguished Young Scholars Program, Type B) in 2014.

Contact Person: Lin Hongwei  hwlin@zju.edu.cn