Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 Spring 2022

Speaker:  Christin Bibby, Lousiana State University
Title: Matroid schemes and geometric posets
Time: 2:30 PM, Monday, April 25, 2022
Place: ZOOM

Abstract: The intersection data of an arrangement of hyperplanes is described by a geometric lattice, or equivalently a simple matroid. There is a rich interplay between this combinatorial structure and the topology of the arrangement complement. In this talk, we will similarly characterize the combinatorial structure underlying certain arrangements of subvarieties by defining a class of geometric posets and a generalization of matroids called matroid schemes. Notions such as the independence complex and the Tutte polynomial extend to this setting, and we will touch on the topological implications of this framework.


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