Special year - math workshop

Sponsored by Dr. John P. Hempel 

Organizers: Matt Baker, Chris Eur, June Huh, Oliver Lorscheid, and Felipe Rincon

This event aims to bring together leading researchers in different areas of combinatorial geometry. This workshop is a part of the...

Abstract: A toric vector bundle is a torus equivariant vector bundle on a toric variety.

We begin by recalling the classification of toric vector bundles due to Klyachko. The Klyachko data of a toric vector bundle can be interpreted as a "piecewise...

Abstract: After a gentle introduction to matroids, I will present parts of a new OSCAR software module for matroids through several examples. I will focus on computing the moduli space of a matroid which is the space of all arrangements of...

Abstract: The foundation of a matroid is an algebraic invariant that controls representations over any partial field, hyperfield, or more generally, any pasture. We show that, under certain conditions, the foundation of a generalized parallel...

Abstract: This talk asks which tropicalisations of subvarieties of the torus know the cohomology of the original variety. A motivating example are linear embeddings of complements of hyperplane arrangements. 

We can prove that the tropicalisation...

Abstract: We characterize the topology of the space of Lorentzian polynomials with a given support in terms of the local Dressian. We prove that this space can be compactified to a closed Euclidean ball whose dimension is the rank of the Tutte group...

Abstract: We study the tropicalization of principal minors of positive definite matrices over a real valued field. This tropicalization forms a subset of M-concave functions on the discrete n-dimensional cube. We show that it coincides with a linear...

Abstract: The groundbreaking results by Huh (further extended in joint work with Adiprasito and Katz) allowed to associate to a matroid a class in the Chow ring of the permutohedral variety. The technique turned out to be especially powerful, as...

Abstract: I will introduce the external activity complex of an ordered pair of matroids on the same ground set. This is the combinatorial analogue of the Schubert variety of an ordered pair of linear subspaces of a fixed space, which is also new...

Abstract: I will share with you a connection between multimatroids and moduli spaces of rational curves with cyclic action. Multimatroids are generalizations of matroids and delta-matroids that naturally arise from topological graph theory. The main...