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.