# Video Lectures

### Non-Orientable Lagrangian Fillings of Legendrian Knots

Most work on Lagrangian fillings of Legendrian knots to date has concentrated on orientable fillings, but instead I will present some first steps in constructions of and (especially) obstructions to the existence of (decomposable exact) non...

### Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions

We study Chern-Simons theories at large N with either bosonic or fermionic matter in the fundamental representation. The most fundamental operators in these theories are mesonic line operators, the simplest example being Wilson lines ending on...

### Set Chasing, with an application to online shortest path

Sébastien Bubeck

Since the late 19th century, mathematicians have realized the importance and generality of selection problems: given a collection of sets, select an element in each set, possibly in a nice” way.  Of particular importance in computer science is the...

### Singular plane curves and stable nonsqueezing phenomena

The existence of rational plane curves of a given degree with prescribed singularities is a subtle and active area in algebraic geometry. This problem turns out to be closely related to difficult enumerative problems which arise in symplectic field...

### Non-vanishing of twists of GL(4) L-functions

Liyang Yang

I will discuss recent work with Maksym Radziwill in which we show that for any fixed tempered cuspidal representation π of GL(4) over the rationals, there exist infinitely many primitive characters χ such that the twisted L-function L(s,π×χ) is non...

### Black hole searches for ultralight bosons

Masha Baryakhtar

I will discuss how black holes can become nature's laboratories for ultralight axions. When a boson's Compton wavelength is comparable to the horizon size of a black hole, energy and angular momentum from the black hole are converted into...

### Arithmetic and Dynamics on Varieties of Markoff Type

The Markoff equation x2+y2+z2=3xyz, which arose in his spectacular thesis (1879), is ubiquitous in a tremendous variety of contexts.  After reviewing some of these, we will discuss joint work with Bourgain and Sarnak establishing forms of strong...

### Invariant Gibbs measures for the cubic nonlinear wave equation

In this talk, we prove the invariance of the Gibbs measure for the three-dimensional cubic nonlinear wave equation, which is also known as the hyperbolic Φ43-model.

In the first half of this talk, we illustrate our main objects and questions...

### Sailing Past the Edge and Discovering the Island

Tarek Anous

Quantum extremal surfaces and islands have led us to rethink the very meaning of microscopic entropy in the presence of dynamical gravity. I will present some work elucidating how the island/QES prescription emerges in a simple doubly holographic...

### Multi-group fairness, loss minimization and indistinguishability

Parikshit Gopalan

Training a predictor to minimize a loss function fixed in advance is the dominant paradigm in machine learning. However, loss minimization by itself might not guarantee desiderata like fairness and accuracy that one could reasonably expect from a...