# Video Lectures

In certain time-dependent backgrounds there are nonstandard light strings that are created classically at an instant and cannot be approximated by particles. We discuss the implications of these strings to black holes and cosmology.

Through the random matrix analogy, Fyodorov, Hiary and Keating conjectured very precisely the typical values of the Riemann zeta function in short intervals of the critical line, in particular their maximum. Their prediction relied on techniques...

In Euclidean geometry, bisectors are perpendicular lines. In random plane geometry, the situation is more complicated. I will describe bisectors in the directed landscape, the universal geometry in the KPZ class. These help answer some open...

For a compact subset K of a closed symplectic manifold, Entov-Polterovich introduced the notion of (super)heaviness, which reveals surprising symplectic rigidity. When K

is a Lagrangian submanifold, there is a well-established criterion for its...

Centers of galaxies are fertile environments for a variety of dynamical processes, owing to the high density of stars and the presence of a central supermassive black hole. Stars may occasionally be deflected onto a deadly trajectory, passing too...

The Mackey-Zimmer representation theorem is a key structural result from ergodic theory: Every compact extension between ergodic measure-preserving systems can be written as a skew-product by a homogeneous space of a compact group. This is used, e.g...

Let X be a smooth projective variety over the field of complex numbers. The classical Riemann-Hilbert correspondence supplies a fully faithful embedding from the category of perverse sheaves on X to the category of algebraic D_X-modules. In this...

In this talk, I will describe recent progress on moduli stabilization in string theory. In particular, I will describe recently found supersymmetric AdS_4 vacua, with exponential scale separation, of type IIB string compactifications on O3/O7...

Define the Collatz map Col on the natural numbers by setting Col(n) to equal 3n+1 when n is odd and n/2 when n is even. The notorious Collatz conjecture asserts that all orbits of this map eventually attain the value 1. This remains open, even if...

A central goal of physics is to understand the low-energy solutions of quantum interactions between particles. This talk will focus on the complexity of describing low-energy solutions; I will show that we can construct quantum systems for which the...