Olivetti Club

Jeffrey JiangCornell University
Unexpected applications of pants

Tuesday, September 14, 2021 - 4:35pm
Malott 406

A topological quantum field theory (TQFT) is a theory in which a mathematician gets funding to draw pictures of pants and pasta by inserting the word "quantum" into the name of a mathematical object of interest. In this talk, I hope to define a TQFT and look at the special case of 2 dimensions, in which case there is a nice correspondence with an algebraic gadget called a Frobenius algebra. The ultimate goal will be to sketch the construction of a specific TQFT using a finite group G, and to use pants to derive Mednykh's formula, which is a formula for counting the number of group homomorphisms from the fundamental group of a closed surface to G.