Video Lectures

The law of Aboav--Weaire and extensions

December 10, 2014

In two-dimensional grain structure, one observes that grains with a small number of sides tend to be surrounded by grains with a large number of sides, and vice-versa. The Law of Aboav--Weaire gives this observation a mathematical formulation, that...

video lecture

Topological similarity of random cell complexes, and applications

December 10, 2014

Benjamin Schweinhart

Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. I'll introduce the notions of a 'swatch' and a 'cloth', which provide a...

video lecture

Beyond linear algebra

December 10, 2014

Bernd Sturmfels

video lecture

The Andre-Oort conjecture II

December 10, 2014

Bruno Klingler

The Andre-Oort conjecture describes the expected distribution of special points on Shimura varieties (typically: the distribution in the moduli space of principally polarized Abelian varieties of points corresponding to Abelian varieties with...

video lecture

A support theorem for the Hitchin fibration

December 09, 2014

Pierre-Henri Chaudouard

The main tool in Ngô's proof of the Langlands-Shelstad fundamental lemma, is a theorem on the support of the relative cohomology of the elliptic part of the Hitchin fibration. For $\mathrm{GL}(n)$ and a divisor of degree $> 2g-2$, the theorem says...

video lecture

More on sum-of-squares proofs for planted clique

December 09, 2014

Avi Wigderson

While this talk is a continuation of the one I gave on Tue Nov 25, it will be planned as an independent one. I will not assume knowledge from that talk, and will reintroduce that is needed. (That first lecture gave plenty of background material, and...

video lecture

Ball quotients

December 08, 2014

Bruno Klingler

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...