Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: A Survey of Riemann-Roch in Tropical Geometry
Seminar | September 19 | 3:45-4:45 p.m. | 939 Evans Hall
Chris Eur, UC Berkeley
Many 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) Riemann-Roch 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 Hirzebruch-Riemann-Roch on wonderful compactifications, and discuss some of its properties both algebraic and combinatorial.