Szego Seminar: Fermionic Calculus and its application

Speaker: Ching-Chia Hsu, Washington University in St. Louis

Abstract: For the usual calculus we learned from undergraduate, all the variables commute. How do we define the calculus for the variables that are fermionic, i.e., variables that anti-commute with each other. Extracting some properties from the indefinite integral, the rules of calculus for these fermionic variables are surprisingly simple. After introducing these simple formulae in fermionic calculus, we will talk about Mathai-Quillen (1986) formalism for Thom class in the language of superspace. After giving the construction for Thom class, we can provide a very short proof for the Gauss-Bonnet-Chern Theorem and Poincare-Hopf Theorem. 

Pizza will be provided.