Special Year Seminar II

In this talk, I will describe a new definition, joint with Bivas Khan, for a tropical toric vector bundle on a tropical toric variety. This builds on the tropicalizations of toric vector bundles, and can be used to define tropicalizations of vector bundles on subvarieties of toric varieties.  The key combinatorial input is a valuated matroid, which defines a tropical linear space that in the realizable case is the tropicalization of the fiber over the identity of the torus.