Suspected En-algebras and their higher representations in topological orders

Abstract

Higher dimensional or categorical algebras and their higher representations are recently widely used in the study of topological orders. In this expository talk I introduce the geometric intuitions behind those applications, present a periodic table of those higher algebras, and introduce J. Lurie's notion of center of higher algebras which is fundamental for understanding their higher representations. If time permits, I will also talk about how to apply center to topological orders. The higher algebras appearing in this talk are conjecturally special cases of En-algebras whose definition is given by Lurie based on the work of May, Boardman-Vogt, Dunn and others.