Algebraic Geometry Seminar

Yoav Len, Department of Combinatorics & Optimization, University of Waterloo

"Combinatorial Hodge Theory"

Our seminar will follow the paper "Hodge theory for combinatorial geometries" by Adiprasito--Huh--Katz. The main result is a proof of Rota's conjecture on the log concavity of the characteristic polynomial of arbitrary matroids. This generalizes the log concavity of both the chromatic polynomial of a graph and of the f-vector of a realizable matroid. In this first talk, I will introduce some of the ideas that show up in the paper such as matroids, chromatic polynomials, and Chow groups. I will explain how they fit together, and give an overview of the main results.

MC 5403