Back to Departmental Colloquium: Spring 2022
Departmental Colloquium
Date: Thursday, Feb 24, 2022
Time: 4:00PM
Location: JWB 335
Robin Pemantle
University of Pennsylvania
Title |
ACSV - an adventure in combinatorics through many foreign lands, such as analysis, algebraic geometry and topology |
Abstract |
Analytic Combinatorics in Several Variables (ACSV) seeks to estimate coefficients of Laurent series F(x,y,z) where the series has some nice form. Motivation comes from many corners of combinatorics and discrete probability theory, including random walks, lattice paths, quantum walks, random tilings, and many other “exactly solvable” models, i.e., models for which closed form generating functions exist. The general solution to the coefficient estimation problem requires a combination of techniques from harmonic analysis, computer algebra / algebraic geometry and algebraic topology, specifically stratified Morse theory and singularity theory. The title of this talk borrows from our 2019 AMS Notices article, in advance of the recent AMS-sponsored Math Research Community on ACSV. In this talk for a general math audience, I will amplify on the motivation for the problem of coefficient extraction, show pictures of diverse phenomena, provide a map of the areas of math intersected by the problem, and give an idea of the main constructions, arguments and results. |
Probability