Combinatorial atlas for log-concave inequalities

Abstract: The study of log-concave inequalities for combinatorial objects have seen much progress in recent years. One such progress is the solution to the strongest form of Mason’s conjecture (independently by Anari et. al. and Brándën-Huh). In the case of graphs, this says that the sequence $f_k$ of the number of forests of the graph with $k$ edges, form an ultra log-concave sequence. In this talk, we discuss an improved version of all these results, proved by using a new tool called the combinatorial atlas method. This is a joint work with Igor Pak. This talk is aimed at a general audience.

commutative algebraalgebraic geometrycombinatorics

Audience: researchers in the topic

Matroids - Combinatorics, Algebra and Geometry Seminar