Video Lectures

What edge density of a graph guarantees that that it will contain a particular subgraph? Or one of a given family F of subgraphs? The celebrated Erdős--Stone--Simonovits Theorem characterizes the maximum edge density in F-free graphs, in terms of...

We are surrounded by functional networks, from fluid transport in plants and animals to macroscopic elastic scaffoldings and microscopic crystals and materials, and engineered power grids. Often, such networks can be seen as optimized for their...

We study configurations of disjoint Lagrangian submanifolds in certain low-dimensional symplectic manifolds from the perspective of the geometry of Hamiltonian maps. We detect infinite-dimensional flats in the Hamiltonian group of the two-sphere...

The talk discusses basics of quantum groups at roots of unity with motivation from modular representation theory.

Faltings proved the statement, previously conjectured by Shafarevich, that there are finitely many abelian varieties of dimension nn, defined over a fixed number field, with good reduction outside a fixed finite set of primes, up to isomorphism. In...

I will start with a few comments on the proof of the equivalence presented in the previous talks. Then I will focus on the description of the abelian category of perverse sheaves on the affine flag variety on the coherent side, where the answer is...

We argue that quantization, a mathematical model of the quantum classical correspondence, gives rise to approximate unitary representations of symplectomorphism groups. As an application, we get an obstruction to symplectic action of Lubotzky...

Bernstein's theorem (also known as the Bernstein-Khovanskii-Kushnirenko theorem) gives a bound on the number of nonzero solutions of a polynomial system of equations in terms of the mixed volume of its Newton polytopes. In this talk, we will give...

In 2017 Lucio Galeati understood that a suitable scaling limit of certain hyperbolic PDEs with noise may lead to deterministic parabolic equations. Since then, in collaboration with Lucio and Dejun Luo, we have understood the phenomenon from several...

I revisit the basic statistical problem of estimating the mean of a real-valued distribution. I will introduce an estimator with the guarantee that "our estimator, on *any* distribution, is as accurate as the sample mean is for the Gaussian...