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: 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: 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: 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: 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.
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: 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: 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...
Summary: This event aims to foster
collaboration between combinatorialists and amplitudologists in two
ways: first by bridging language and concept barriers, and second
by highlighting open problems of mutual interest.
