Alexi Hoeft (VCU)
Witten's conjecture, Feynman's theorem and the combinatorics of ribbon graphs.
In 1991, Witten conjectured a connection amongst the worlds of moduli spaces, nonlinear partial differential equations, and the matrix models of theoretical physics and he provided physical reasoning (i.e. a ''physics proof'') of its validity. Within a year, Kontsevich published a mathematically rigorous proof of the conjecture, and this work contributed to his 1998 Fields Medal. This talk will focus on tools used in the matrix model corner of Kontsevich's proof. After reviewing background material and the context of the problem, we will explore the combinatorics in a related theorem of Feynman which allows us to count the number of so-called ribbon graphs or schematic setups of a physical situation.