SEMINAR: Groups and Combinatorics Seminar, Counting surfaces: ribbon graphs, branched covers, and more

Norman Do (Monash University)

will speak on

Counting surfaces: ribbon graphs, branched covers, and more

at 3pm Friday 5 September in Weatherburn Lecture Theatre.

Abstract:

The enumeration of ribbon graphs (graphs embedded in surfaces) satisfies a so-called Tutte recursion, while the enumeration of branched covers (maps from a surface to a sphere) satisfies a so-called cut-and-join recursion. In fact, both are instances of the topological recursion, which emerged several years ago from the theory of matrix models. The topological recursion is now known to govern myriad problems from enumerative geometry, knot theory, theoretical physics, and more. We will give a very gentle introduction to these ideas, focusing on the combinatorial and algebraic aspects.