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
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.