Alex Fink, Queen Mary University of London

Abstract

In 2008, looking to bound the face vectors of tropical linear spaces, Speyer introduced the g-invariant of a matroid. He proved its coefficients nonnegative for matroids representable in characteristic zero and conjectured this in general. After introducing these objects, this talk will give an overview of the ingredients in recent work with Andrew Berget that proves the conjecture.  A main character is the variety of coordinatewise quotients of points in two linear subspaces, and its initial degenerations which encode a new generalization of external activity to a pair of matroids.

See: https://sites.google.com/view/rutgersdmseminar