Abstract: 

In algebraic topology, all homology and cohomology groups are homotopy groups of spectra, a perspective known for a half century.  How do we get spectra that represent interesting homology and cohomology theories? One way is by infinite loop space theory, the concrete precursor of lnfinity categories. I will explain what infinite loop space theory is and describe the operadic approach to it.

Introduction of the speaker:

Professor J. Peter May is a professor at University of Chicago. He is a world famous algebraic topologist, and a member of the inaugural class of Fellows of the American Mathematical Society (AMS). He has made foundational and groundbreaking contributions to many subjects in algebraic topology and homotopy theory, such as the computations of 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. Professor 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, which include a very influential undergraduate textbook "A Concise Course in Algebraic Topology".

Professor May had served for many years as the chair of the Department of Mathematics at University of Chicago and the graduate admission and study committees. Professor May values very highly of education in mathematics. Since the year 2000, he has been organizing every year the undergraduate summer research program at University of Chicago, also known as the REU; Until the year 2019, he has advised more than 60 doctoral students, many of which have held tenured positions in prestige universities all over the world. Professor May has made significant contributions to algebraic topology in China, especially in educating young Chinese algebraic topologists. Many students who got their bachelor's degrees from Peking University have got or are pursuing their Ph.D. degrees under the guidance of Professor May, such as Zhouli Xu, Foling Zou, Jia Kong and Weinan Lin, or have been greatly influenced by Professor May, such as Yifei Zhu, Guozhen Wang, Guchuan Li and Yunze Lu.

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