Colloquium: Dr. Eugenia Cheng

UW-Milwaukee Department of Mathematical Sciences presents,
Dr. Eugenia Cheng;
Senior Lecturer
University of Sheffield & School of the Art Institute of Chicago

Thursday April 7, 2016
12:30pm in EMS E495

From loop spaces to n-categories

Operads were originally introduced as a powerful tool for handling the “weak monoid” structure of loop spaces, and we will show how to harness this same power to handle the structure of weak n-categories according to the work of Trimble and Batanin, with further developments by Leinster and Cheng. It is known that n-groupoids are too strict to model homotopy n-types, and instead we must use “weak n-groupoids”, whose axioms are only satisfied up to equivalence, as in weak monoids. The problem is to make this definition in a coherent way; these equivalences must satisfy some other axioms of their own, possibly only up to equivalence. In this talk we will discuss how to approach this problem using operads. The talk will be introductory; in particular no knowledge of n-categories will be assumed.