Characteristic sets of matroids and one-dimensional groups

Algebra Seminar
Monday, January 23, 2023 - 10:20am for 1.5 hours (actually 80 minutes)
Skiles 005
Dustin Cartwright – University of Tennessee – cartwright@utk.edu
Abeer Al Ahmadieh

Algebraic matroids record the algebraic dependencies among elements in a field extension, similar to the linear dependencies of vectors in a vector space. Realizing a given matroid by elements in a field extension can depend on the characteristic of the field. I will talk about the possible characteristic sets of algebraic matroids. An essential tool is the one-dimensional group construction of an algebraic matroid, which turns the realization problem for algebraic matroids into a linear problem over the endomorphism ring of a one-dimensional algebraic group.