Speaker: Jie Wu (吴杰， BIMSA)

Time: 17:00-17:45, 2024-12-09

Venue: A6-1

Zoom: 388 528 9728

Password: BIMSA

Abstract

The high-order interaction phenomena occur popularly in data analytics. The good progress for scientific and mathematical understanding on high order interaction complex system may highly influence the future development of the artificial intelligence. Guided by this scientific problem, various new topological theories have been recently developed from GLMY homology of digrahs as topological tools for analysing high order structures of complex networks, which enrich GLMY theory---a new-born research field in algebraic topology---that has achieved fruitful successful applications in complex diseases, microbiology, molecular and materials sciences. In this talk, we will give an introduction to the topological approaches to the mathematical modelings for high-order interaction complex systems, particularly the GLMY homology and its variants as effective tools in analysing topological structures of mathematical modelings beyong traditional simplicial complex modeling such as hypergraph modeling and the newly proposed statistical modelings of IdopNetwork and HyperNetwork. The talk will aim to general audience with highlingting how the interdisciplinary research collaboration with the statistics team would lead to the successful applications of topology with receiving returns to mathematics for developing GLMY theory.

Speaker Intro

Jie Wu received a Ph.D. degree in Mathematics from the University of Rochester and worked as a postdoc at Mathematical Sciences Research Institute (MSRI), University of California, Berkeley. He was a former tenured professor at the Department of Mathematics, National University of Singapore. In December 2021, he joined the Yanqi Lake Beijing Institute of Mathematical Sciences and Applications (BIMSA). His research interests are algebraic topology and applied topology. The main achievements in algebraic topology are to establish the fundamental relations between homotopy groups and the theory of braids, and the fundamental relations between loop spaces and modular representation theory of symmetric groups. In terms of applied topology, he has obtained various important results on topological approaches to data science. He has published more than 90 academic papers in top mathematics journals such as the Journal of American Mathematical Society, Advances in Mathematics, etc. In 2007, he won the "Singapore National Science Award. In 2014, his project was funded by the Overseas Joint Fund of National Natural Science Foundation (Jieqing B).

Member Seminar Intro

The BIMSA member seminar is a weekly event during which researchers engage in discussions about their extensive research interests, addressing a diverse audience that includes fellow researchers and all postdoctoral scholars within the institute. This forum provides a unique privilege and an invaluable opportunity for each research faculty member, serving as a speaker, to introduce their research field, promote the subject within the institute, and ignite the potential for future collaborations with other research groups within the institute.

The lecture format consists of a 30-minute colloquium-style presentation, thoughtfully tailored to be accessible to postdoctoral scholars and researchers from diverse disciplines within the institute. Following the presentation, a 15-minute discussion session is anticipated, involving active participation from postdocs representing various fields.

It is mandatory for all postdocs at the institute to actively participate in this event. The enthusiastic involvement of faculty members is greatly valued and will prove mutually beneficial for both the speaker and the junior audience.

Organizers

Yuval Peres

Professor

Probability Theory

Artan Sheshmani

Professor

Algebraic Geometry

Hossein Yavartanoo

Professor

Mathematical Physics