IMath Seminar: Dr. Oleg Evnin

You are all invited to a seminar featuring Dr. Oleg Evnin (Department of Physics, Faculty of Science Chulalongkorn University, Thailand). This is an in-person event and it will be held on Monday, 16 December 2024, 10:00 to 11:00 AM at the Math Bldg MB 300.

Title: A Gaussian integral that counts regular graphs

Abstract: Counting regular graphs (where all the vertices have the same degree) is an old, and rather intricate, combinatorial problem. No closed-form expression is known, while many powerful asymptotic estimates have been obtained. I revisit this problem from an angle typical of mathematical statistical physics,and use a set of auxiliary variables to express the number of d-regular graphs on N vertices as a d-dimensional Gaussian integral. In terms of this integral, recovering the asymptotic formulas at large N reduces to an explicit saddle point problem. The techniques used in this approach create contacts with more sophisticated problems involving random walks and spectra of regular graphs with degree constraints.