Video Lectures

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 hyperplanes with...

Computational problems exhibit a diverse range of behaviors in terms of how quickly and effectively they can be solved.  What underlying mathematical structure (or lack thereof) in a computational problem leads to an efficient algorithm for solving...

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 linear map"...

We analyze a model of qubits which we argue has an emergent quantum gravitational description similar to the fermionic Sachdev-Ye-Kitaev (SYK) model. The model we consider is known as the quantum $q$-spin model because it features $q$-local...

Associated to a star-shaped domain in ℝ2nR2n are two increasing sequences of capacities: the Ekeland-Hofer capacities and the so-called Gutt-Hutchings capacities. I shall recall both constructions and then present the main theorem that they are the...

In the early 2000's, Bertolini and Darmon introduced a new technique to bound Selmer groups of elliptic curves via level raising congruences. This was the first example of what is now termed a "bipartite Euler system", and over the last decade we...

Multi-variate residues on Grassmannians G(k,n) and moduli spaces M0,n are ubiquitous in the study of scattering amplitudes; they provide a powerful and essential tool. Amenable theories include the biadjoint scalar, NLSM, Yang-Mills, gravity and N=4...

A classical construction associates a Poincare duality algebra to a homogeneous polynomial on a vector space. This construction was used to give a presentation for cohomology rings of complete smooth toric varieties by Khovanskii and Pukhlikov and...

For every surface S, the pure mapping class group G_S acts on the (SL_2)-character variety Ch_S of a fundamental group P of S. The character variety Ch_S is a scheme over the ring of integers. Classically this action on the real points Ch_S(R) of...