Combinatorics of planar triangulations and quantum topology

Slava Krushkal (UVa)

Abstract. In the 1960s Tutte observed that the value of the chromatic polynomial of planar triangulations when the parameter equals (golden ratio +1) obeys a number of remarkable properties. In this talk I will explain how quantum topology (TQFT) gives rise to a conceptual framework for studying planar triangulations. (No prior knowledge of TQFT will be assumed.) I will discuss several extensions of Tutte’s results and applications to the structure of both classical and quantum polynomials of graphs. This talk is based on joint works with Ian Agol and with Paul Fendley.