Title: h-vector inequalities for weak maps of matroids
Speaker: Alex Mason (University of Washington)
Speaker's URL: https://math.washington.edu/people/alexander-mason
Abstract: The study of matroids and their invariants has undergone remarkable developments in recent years. In particular, many long-standing conjectures concerning inequalities that are satisfied between certain invariants, such as the number of flats of a given rank, associated to a given matroid, have been resolved. We take a different perspective and consider inequalities between invariants of different matroids. By employing combinatorial and algebraic methods, we prove several results, with our main result being that the flag h-vector is nonincreasing under weak maps. The talk is intended to be accessible to graduate students.
URL associated with Seminar: https://u.osu.edu/probability/autumn-2023/