Title: Hodge Theory in Combinatorics
Speaker: Evan Nash (The Ohio State University)
Abstract: In 1968, Read conjectured that the coefficients of the chromatic polynomial of a (finite) graph form a log concave sequence. Over 40 years later Adiprasito, Huh, and Katz provided a proof of this conjecture using purely combinatorial methods. What makes this story interesting is that the ideas they used were inspired by constructions from algebraic geometry. Their technique is to develop a Hodge theory for matroids, which are generalizations of graphs. Proving analogs of theorems from algebraic geometry, they are able to deduce Read's conjecture. We will give a few snippets of this conversation between the two fields.
Seminar URL: http://mgsa.org.ohio-state.edu/home.html
