Fields Medal Lecture Series
Date: Friday, March 17, 2023
Time: 2:00 pm to 3:00 pm
Venue: Seminar Hall
Log-concavity in combinatorics: the work of June Huh
S. Viswanath
Institute of Mathematical Sciences, Chennai.
17-03-23

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Abstract

In 2010, while still a graduate student, June Huh stunned the mathematical world with his proof of Read's celebrated unimodality conjecture for chromatic polynomials of graphs. Together with his partial proof of the Heron-Rota-Welsh log-concavity conjecture for characteristic polynomials of matroids, this constituted a major advance on conjectures that had resisted four decades of effort.

Huh and collaborators followed this up with numerous striking results for general matroids - log-concavity of the characteristic polynomial, ultra log-concavity of the f-polynomial and the Dowling-Wilson conjecture, among others. I will present an overview of these theorems, with a focus on the combinatorial side. Huh's methods now constitute the new area of "Hodge theory in combinatorics", and I will make brief comments on these. The talk will be widely accessible, with minimal prerequisites.