Tropical Ehrhart theory

Ehrhart theory, a.k.a. counting lattice points in lattice polytopes, is a bread-and-butter topic in algebraic combinatorics.  Developing Ehrhart theory in a generalized setting of tropical geometry is an emerging endeavor at the intersection of algebraic geometry and matroid theory.  I will describe a foundational result that opens the door to many new directions.  Our results resolve a conjecture of Tohaneanu and give a new proof of the nonnegativity of the omega invariant in support of Speyer's f-vector conjecture.  Joint work with Alex Fink and Matt Larson.