Abstract

Equivariant multiplicative infinite loop space theory is interesting, but hard.  I will describe definitions in terms of symmetric groups which promise to give an easy new way to build the theory.  As I shall describe, the main obstruction to making the new theory rigorous is the elementary categorical combinatorics of symmetric groups.

Biography

Prof. May is a professor at the University of Chicago. He is a world-famous algebraic topologist and a member of the inaugural class of Fellows of the American Mathematical Society. He has made foundational and groundbreaking contributions to many subjects in algebraic topology and homotopy theory, such as computation of the stable homotopy groups of spheres, the May spectral sequences, theory of generalized cohomology operations, infinite loop space theory, equivariant homotopy theory, highly structured ring spectra theory, theory of operads, parametrized homotopy theory, theory of model categories, etc. Prof. May has published more than 100 papers in leading mathematical journals, such as the Annals of Mathematics. He has also written many books in homotopy theory, including a very influential textbook, A concise course in algebraic topology. He had served for many years as the chair of the Department of Mathematics at the University of Chicago, as well as on its graduate admissions and studies committees. Prof. May values education in mathematics very highly. Since 2000, he has been organizing every year the undergraduate summer research program at the University of Chicago, also known as the REU. Until 2024, he has advised more than 60 doctoral students, many of whom have held tenured positions in prestigious universities all over the world. Prof. May has made a significant contribution to the development of algebraic topology in China, especially in educating and influencing a younger generation of Chinese algebraic topologists.