# Video Lectures

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...

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...

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...

One of the most important events in science dates back to 1687,
when Newton published the *Philosophiæ Naturalis
Principia Mathematica*. In this masterpiece of human
thought, the famous second law of motion is laid out, which
concretely and...

We will discuss a version of the Green--Tao arithmetic regularity lemma and counting lemma which works in the generality of all linear forms. In this talk we will focus on the qualitative and algebraic aspects of the result.

Liouville conformal field theory is a CFT with central charge c>25 and continuous spectrum, its correlation functions on Riemann surfaces with marked points can be expressed using the bootstrap method in terms of conformal blocks. We will explain...