Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: First Steps towards Tropical Hirzebruch-Riemann-Roch

Seminar | September 19 | 3:45-4:45 p.m. | 939 Evans Hall | Canceled

 Christopher Eur, UC Berkeley

 Department of Mathematics

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 discuss how these may hint at the tropical version of Hirzebruch-Riemann-Roch (HRR), and finish with the speaker's first attempts towards tropical HRR with potential applications to algebraic geometry and combinatorics.