Title: Combinatorial Applications of Computational Topology and Algebraic Geometry
This talk is about an area known as Analytic Combinatorics in Several Variables (ACSV), which uses complex analytic techniques to obtain asymptotics for combinatorial problems in which a multivariate generating function is known. More abstractly, one solves the problem of estimating the Taylor coefficients of a
multivariable rational function P(z_1, …, z_d) / Q(z_1, … , z_d).
I will begin with a short overview of how it all works, and some examples of the use of ACSV to prove limit shape theorems in combinatorics and statistical mechanics. Next I will discuss the obstacles to automating these analyses, which have to do with explicit computation of cycles in algebraic varieties. Lastly I will present some recent results and conjectures.
Joint work with Yuliy Baryshnikov and Steve Melczer
Wednesday, November 7, 4:30 – 5:30 p.m.
Tea will be served at 4:00 p.m.