Seminars Sorted by Series

Sponsored by Dr. John P. Hempel 

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

This event brought together leading researchers in different areas of combinatorial geometry. This workshop was a part of the special...

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...

Abstract: In this talk, I will first review previous works on matroid representations initiated by Tutte in 1958, generalized by Dress and Wenzel in the 1980s, and refined by Baker, Bowler, and Lorscheid more recently using the language of F1...

Abstract: Baker and Bowler (2019) showed that the Grassmannian can be defined over a tract, a field-like structure generalizing both partial fields and hyperfields.

This notion unifies theories for matroids over partial fields, valuated matroids, and...

Abstract: Delta matroids are a generalization of matroids, encompassing combinatorial structures such as matchings of graphs and principal minors of symmetric matrices. In this talk, I will discuss a notion of valuated Delta matroids and their...

Abstract: The derived category of a variety is an important and difficult invariant. In this talk, I discuss a purely convex-geometric and combinatorial approach to these categories for toric varieties. Along the way, we will run into the curious...

Abstract: Grassmannians and flag varieties are important moduli spaces in algebraic geometry. Quiver Grassmannians are generalizations of these spaces arise in representation theory as the moduli spaces of quiver subrepresentations. These represent...

Abstract: Delta-matroids are "type B" or "type C" analogues of matroids. I will discuss how to extend a geometric construction related to matroids to delta-matroids. Using this construction, we prove the ultra log-concavity of the number of...