Video Lectures

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...

The future interior of black holes in AdS/CFT can be described in terms of a quantum circuit. We investigate boundary quantities detecting properties of this quantum circuit. We discuss relations between operator size, quantum complexity, and the...

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...

Many space and astrophysical plasmas, such as the solar wind, radiatively inefficient accretion flows onto black holes, and the intracluster medium of galaxy clusters (ICM), are hot and dilute, which makes them weakly collisional or even...

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...

This is a continuation of a series of talks I have given in recent years reporting on work with Jan Manschot, et. al.
There will be some repetition, and some updates and new results.   (See below for some relevant links.)
Manschot and I have...