**Title: Combinatorial Applications of Computational Topology and Algebraic Geometry**

**Abstract:**

This talk is about an area known as Analytic Combinatorics inĀ 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 inĀ 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.

Mathematics 520

Tea will be served at 4:00 p.m.