CANCELLED - Matroid stratifications of hypergraph determinantal varieties and their realization spaces

Abstract: I will provide an introductory talk to hypergraph determinantal varieties from projective geometry and matroid theory perspectives. I describe their decompositions into matroid varieties. Matroids varieties in general can be reducible with arbitrary singularities by the Mnëv-Sturmfels universality theorem. Our goal is to provide families of matroids whose corresponding varieties are irreducible, and use them to find minimal irreducible decompositions for hypergraph varieties. The main themes of the talk are: 1) giving a decomposition for each hypergraph variety; 2) identifying each component in the decomposition as a matroid variety; and 3) understanding the irreducibility of these matroid varieties and their realizability. I will not assume any prior knowledge of algebraic, polyhedral, or incidence geometry, and I will try to make the talk accessible to people with a broad range of backgrounds. The talk is based on joint work with Oliver Clarke, Kevin Grace, and Harshit Motwani.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html