# Video Lectures

### Galois groups of random integer polynomials

In this three-part lecture series, we will present a series of works by Bedrossian, Blumenthal and Punshon-Smith on the chaotic mixing and enhanced dissipation properties of a passive tracer subject to the motion of an ergodic Markovian flow of...

### Towards Morse theory of dispersion relations

Gregory Berkolaiko

The question of optimizing an eigenvalue of a family of self-adjoint operators that depends on a set of parameters arises in diverse areas of mathematical physics.  Among the particular motivations for this talk are the Floquet-Bloch decomposition...

### Singularity formation for reduced models of fluid equations

The non-resistive electron magnetohydrodynamics (MHD) has some peculiar connection with the Euler equation. Some one-dimensional reduced models are suggested as an attempt to build intuition toward understanding the nonlinear structure and dynamics...

### A Tutorial on Gaussian Elimination

Gaussian elimination is one of the oldest and most well-known algorithms for solving a linear system. In this talk, we give a basic, yet thorough overview of the algorithm, its variants, and standard error and conditioning estimates. In addition, a...

### 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...

### 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...