Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: K-theoretic Tutte polynomials of morphisms of matroids

Seminar | February 4 | 5-6 p.m. | 939 Evans Hall

 Christopher Eur, UC Berkeley

 Department of Mathematics

The Tutte polynomial is among the most important combinatorial invariants of a graph and more generally of a matroid. A geometric interpretation of the Tutte polynomial was given by Fink and Speyer via the K-theory of Grassmannians. In this talk, we define and study the Tutte polynomial of morphisms of graphs and matroids by considering the K-theory of flag varieties. We show that there are two natural generalizations of the Tutte polynomial in this setting, one which is previously known as the Las Vergnas Tutte polynomial and the other which remains combinatorially mysterious. This is joint work with Rodica Dinu and Tim Seynnaeve.