The algebraic geometry of posets

Abstract: Natural poset (partially ordered set) structure arises in polyhedral fans, Coxeter groups, and hyperplane arrangements. In nice cases, there exist stratified algebraic varieties realizing the above poset structures, namely toric varieties, Schubert varieties, and matroid Schubert varieties respectively. I will discuss how to prove combinatorial results using the corresponding algebraic varieties. I will also talk about how to extend the above arguments beyond geometry, for example, the singular Hodge theory of arbitrary matroids. The last part is joint work with Tom Braden, June Huh, Jacob Matherne and Nick Proudfoot.

algebraic geometrynumber theory

Audience: researchers in the topic

UCSB Seminar on Geometry and Arithmetic