Video Lectures

Ball quotients

December 08, 2014

Ball quotients are complex manifolds appearing in many different settings: algebraic geometry, hyperbolic geometry, group theory and number theory. I will describe various results and conjectures on them.

video lecture

Area Laws and the Complexity of Quantum States

December 08, 2014

Umesh Vazirani

One of the great challenges posed by the laws of quantum mechanics is that the number of parameters required to describe a quantum state in general grows exponentially in the number of particles. This complexity is directly related to the phenomenon...

video lecture

Level raising mod 2 and arbitrary 2-Selmer ranks

December 04, 2014

Chao Li

We prove a level raising mod $p = 2$ theorem for elliptic curves over $\mathbb Q$, generalizing theorems of Ribet and Diamond-Taylor. As an application, we show that the 2-Selmer rank can be arbitrary in level raising families. We will begin by...

video lecture

Minimal log discrepancy of isolated singularities and Reeb orbits

December 03, 2014

Mark McLean

Let $A$ be an affine variety inside a complex $N$ dimensional vector space which either has an isolated singularity at the origin or is smooth at the origin. The intersection of $A$ with a very small sphere turns out to be a contact manifold called...

video lecture

Herschel Studies of Extrasolar Kuiper Belt-like Systems

December 02, 2014

Amaya-Moro Martin

Planetesimals are the building blocks of planets. They can be traced by the dust they produce in collisions or sublimation that forms a debris disk. In the solar system, such a dust disk is produced by the asteroids, comets and Kuiper Belt objects...

video lecture

Codimension two cycles

December 02, 2014

Madhav Nori

Problems analogous to Bloch's conjecture, and some tentative methods of attacking them, will be discussed.

video lecture

Taming the hydra: the Word Problem, Dehn functions, and extreme integer compression

December 02, 2014

Timothy Riley

For a finitely presented group, the Word Problem asks for an algorithm which declares whether or not words on the generators represent the identity. The Dehn function is the time-complexity of a direct attack on the Word Problem by applying the...

video lecture

Graphs, vectors and integers

December 01, 2014

Noga Alon

The study of Cayley graphs of finite groups is related to the investigation of pseudo-random graphs and to problems in Combinatorial Number Theory, Geometry and Information Theory. I will discuss this topic, describing the motivation and focusing on...

video lecture

Parallel Repetition From Fortification

December 01, 2014

Dana Moshkovitz

The Parallel Repetition Theorem upper-bounds the value of a repeated (tensored) two prover game in terms of the value of the base game and the number of repetitions. In this work we give a simple transformation on games -- "fortification" -- and...

video lecture

Tracking Planet Footprints in Dusty Disks

November 25, 2014

Catherine Espaillat

We know that most stars, if not all, were once surrounded by protoplanetary disks. How these young disks evolve into planetary systems is a fundamental question in astronomy. Observations of T Tauri stars (TTS) may provide insights into this...