Prerequisite

Algebraic Topology

Abstract

This course will discuss configuration spaces from the views of homotopy theory. The course will consist of three parts. In the first part, we will discuss the motivations of studying configuration spaces in homotopy theory, including the configuration space models for iterated loop spaces, little cube operads, and Hopf invariants. In the second part of the course, we will review some milestone articles on configuration spaces related to homotopy theory. In the final part of the course, we will review the most updated progress on configuration spaces and propose questions on the topic.

Lecturer 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