Jacob Matherne (U. Mass. Amherst)

Singular Hodge Theory of Matroids

Abstract for the Combinatorics and Algebra Seminars
2018 April 10

To any matroid, I will associate a certain ring that, when the matroid is realizable, is the cohomology ring of a certain variety called the semi-wonderful model. I will show how the Hodge theory of this ring can conjecturally be used to establish the "top-heavy conjecture" of Dowling and Wilson from 1974 as well as the non-negativity of the matroid Kazhdan–Lusztig polynomials of Elias, Proudfoot, and Wakefield.

This is joint work with Tom Braden, June Huh, Nick Proudfoot, and Botong Wang.


To the Combinatorics Seminar Web page.