# Video Lectures

### Counting Low Degree Number Fields with Almost Prescribed Successive Minima

Sameera Vemulapalli

The successive minima of an order in a degree n number field are n real numbers encoding information about the Euclidean structure of the order. How many orders in degree n number fields are there with almost prescribed successive minima, fixed...

### The Study of Wave Interactions: Where Beautiful Mathematical Ideas Come Together II

Phenomena involving interactions of waves happen at different scales and in different media: from gravitational waves to the waves on the surface of the ocean, from our milk and coffee in the morning to infinitesimal particles that behave like wave...

### The Study of Wave Interactions: Where Beautiful Mathematical Ideas Come Together

Phenomena involving interactions of waves happen at different scales and in different media: from gravitational waves to the waves on the surface of the ocean, from our milk and coffee in the morning to infinitesimal particles that behave like wave...

### The Erdős-Szekeres problem in three (and higher) dimensions

Finding the smallest integer N=ES_d(n) such that in every configuration of N points in R^d in general position there exist n points in convex position is one of the most classical problems in extremal combinatorics, known as the Erdős-Szekeres...

### Locally Decodable Codes

A Locally Decodable Codes (LDC) is an error correcting code which allows the decoding of a single message symbol from a few queries to a possibly corrupted encoding.  LDCs can be constructed, for example, from low degree polynomials over a finite...

### Non-measurability of the inverse theorem for the Gowers norms

Over a high-dimensional vector space Fnpover a fixed finite field Fp, the inverse theorem for the Gowers norm asserts that a bounded function f on this space that has a large Gowers Uk+1 norm, must necessarily correlate with a phase polynomial e(P)...

### Langevin Dynamics of Yang-Mills in 2D and 3D

Hao Shen

We will discuss stochastic quantization i.e. Langevin dynamic of the Yang-Mills model on two and three dimensional torus. This is described by a Lie algebra valued stochastic PDE driven by space-time white noise. We construct (local) solution to...

### Arnold Conjecture Over Integers

Shaoyun Bai

We show that for any closed symplectic manifold, the number of 1-periodic orbits of any non-degenerate Hamiltonian is bounded from below by a version of total Betti number over Z, which takes account of torsions of all characteristics. The proof...

### Regularity of Vortex and SQG Patches

I will review some recent progress on regularity properties of vortex and SQG patches. In particular, I will present an example of a vortex patch with continuous initial curvature that immediately becomes infinite but returns to (C2) class at all...

### On Furstenberg systems for some aperiodic multiplicative functions

The Chowla conjecture from 1965 predicts that all autocorrelations of the Liouville function vanish. In fact, after an adaptation, the Chowla conjecture was expected to hold for all aperiodic multiplicative functions with values in the unit disc (cf...