Characteristic sets of matroids

Abstract: A matroid is a combinatorial abstraction of the types of dependence relations that appear both as linear dependence in vector spaces and algebraic dependence in field extensions. As not all matroids can be realized in either of these ways, we can define the linear and algebraic characteristic sets of a matroid as the set characteristics of fields over which the matroid is realizable in a vector space or field extension, respectively. The focus of my talk will be the possible characteristic sets of matroids. An important tool will be the construction of algebraic matroids from the ring of endomorphisms of a 1-dimensional connected algebraic group. This is joint work with Dony Varghese.

algebraic geometryalgebraic topologygroup theorynumber theoryrepresentation theory

Audience: researchers in the discipline

Queen Mary University of London Algebra and Number Theory Seminar