Video Lectures

In the Western Hemisphere, monetary exchanges have been documented in Mesopotamia and Egypt since the 3rd millennium BCE, using a variety of mediums such as barley, copper, silver, gold, dates, and wool. By the first millennium BCE, weighed silver...

Expressing combinatorial invariants of matroids as intersection numbers on algebraic varieties has become a popular tool in algebraic combinatorics. Several conjectured inequalities among combinatorial data can be traced back to positivity results...

In 2008, looking to bound the face vectors of tropical linear spaces, Speyer introduced the g-invariant of a matroid, defined in terms of exterior powers of tautological bundles on Grassmannians. He proved its coefficients nonnegative for matroids...

Suppose f is a function with Fourier transform supported on the unit sphere in Rd. Elias Stein conjectured in the 1960s that the Lp norm of f is bounded by the Lp norm of its Fourier transform, for any p>2d/(d−1).  We propose to study this...

Let Y be a symplectic divisor of X, ω. In the Kahler setting, Givental's Quantum Lefschetz formula relates certain Gromov-Witten invariants (encoded by the G function) of X and Y. Given an Lagrangian L in (Y, ω|Y), we can lift it to a Lagrangian L'...

In this talk, we present a new method to solve algorithmic and combinatorial problems by (1) reducing them to bounding the maximum, over x in {-1, 1}^n, of homogeneous degree-q multilinear polynomials, and then (2) bounding the maximum value...

Correlation functions of the average null energy operator provide direct theoretical models of collider experiments, and have played a crucial role in contemporary developments in formal QFT and gravity. Recently it has become possible to directly...

I will explain how to realize a gapped Hamiltonian for a (1+1)d system on the lattice which has a categorical symmetry given by the modules of the 4-dimensional Taft algebra. This category is finite but not a fusion category, a fact that presents...

In the late 1800s, in the course of his study of classical problems of number theory, the young Hermann Minkowski discovered the importance of a new kind of geometric object that we now call a convex set. He soon developed a rich theory for...

The satisfiability problem for Constraint Satisfaction Problems (CSPs) asks whether an instance of a CSP has a fully satisfying assignment, i.e., an assignment that satisfies all constraints. This problem is known to be in class P or is NP-complete...