Homotopy Theory I
Up to time permission, the course will mainly cover the following topics: Eilenberg-MacLane spaces and Postnikov system; H-spaces and co-H-spaces, Hopf algebra; Homology of loop spaces, Bott-Samelson theorem, Dyer-Lashof operations; James construction, Whitehead products, Samelson products, configuration spaces, Snaith Theorem; Cohen group, natural self-transformations of the loop suspension functor, functor A^{min} , decompositions of loops on co-H-spaces; EHP sequences and homotopy groups.
Lecturer
Date
16th March ~ 6th July, 2022
Website
Prerequisite
Algebraic topology (Hatcher's book)
Video Public
Yes
Notes Public
Yes
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 "Singapore National Science Award”. In 2014, his project was funded by the “Overseas Joint Fund of National Natural Science Foundation” (Jieqing B).