The AWM and AMS chapters at UConn are organizing a special sigma seminar on Friday February 23rd. The speaker is Dr. Hana Kong (Institute for Advanced Studies)

Title: Infinite loop space theory and recognition principle

Abstract: In homotopy theory, we think about equivalences instead of equalities. For example, homotopy coherence replaces commutativity under this philosophy. In this context, the study of topological commutative monoids relates to infinite loop space theory. In this talk, I will explain how operads encode homotopy coherent structures. One application is the operadic infinite loop space machine. There are also equivariant and multiplicative enhancements of this machine. In joint work with Peter May and Foling Zou, we fit all into a recognition principle in a more general and axiomatic setting.