3:45PM: A Survey of RiemannRoch in Tropical GeometryChris EurMany recent works in algebraic combinatorics carry the theme of rendering results of classical algebraic geometry in tropical geometry. We first give an overview of three particular lines of work carrying such theme: (1) Hodge theory on matroids by Adiprasito, Huh, and Katz, (2) CSM classes of matroids by de Medrano, Rincón, and Shaw, and (3) RiemannRoch on graphs by Baker, Norine, and others. We then focus on a particular object of a tropical linear variety called the volume polynomial which arises as an application of the usual HirzebruchRiemannRoch on wonderful compactifications, and discuss some of its properties both algebraic and combinatorial.

5:00PM: Matroids, Graphs, and Symbolic Powers of Monomial IdealsCharles WangIt is open in general what conditions imply that the symbolic powers and the usual powers of an ideal in a regular ring coincide. For squarefree monomial (i.e. radical) ideals in a polynomial ring in n variables over a field, there is a combinatorial characterization for when these two powers coincide. In this talk, I will discuss the combinatorial objects that arise in this context, and describe their connection to this question.
