Title: Higher Tor Groups of Matroids
Speaker: Kyle Binder (OSU)
Abstract: The Chow group of a loopless matroid is an important invariant which has been used to resolve important positivity results in matroid theory. Topologically, these Chow groups are the Chow groups of toric varieties associated to the Bergman fan of a matroid; algebraically, they are quotients of the Stanley—Reisner ring of the Bergman fan by the action of an ambient torus. In this talk we will generalize the Chow group of a matroid to what we call the Higher Tor Groups of a matroid. Topologically, these are the homology groups of the corresponding toric variety; algebraically, they are the Tor groups of the Stanley—Reisner ring. We will describe some of the basic properties of these Tor groups and compute the Betti numbers in the case of uniform matroids.
