Video Lectures

Natural algorithms for flow problems

April 06, 2015

Nisheeth Vishnoi

In the last few years, there has been a significant interest in the computational abilities of Physarum Polycephalum (a slime mold). This drew from a remarkable experiment which showed that this organism can compute shortest paths in a maze...

video lecture

Proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing a field

March 31, 2015

Ivan Panin

Let $R$ be a regular semi-local domain, containing a field. Let $G$ be a reductive group scheme over $R$. We prove that a principal $G$-bundle over $R$ is trivial, if it is trivial over the fraction field of $R$. If the regular semi-local domain $R$...

video lecture

The Physics of Radiation-Driven Outflows in Active Galactic Nuclei

March 31, 2015

Daniel Proga

I review the physics of launching, acceleration, and propagation of radiation driven winds. I will consider two kinds of outflows powered by radiation emitted from the AGN central engine: (1) outflows driven from the innermost part of a black hole...

video lecture

Kolmogorov width of discrete linear spaces: an approach to matrix rigidity

March 31, 2015

Sergey Yekhanin

A square matrix $V$ is called rigid if every matrix obtained by altering a small number of entries of $V$ has sufficiently high rank. While random matrices are rigid with high probability, no explicit constructions of rigid matrices are known to...

video lecture

On the geometry and topology of zero sets of Schrödinger eigenfunctions

March 30, 2015

Yaiza Canzani

In this talk I will present some new results on the structure of the zero sets of Schrödinger eigenfunctions on compact Riemannian manifolds. I will first explain how wiggly the zero sets can be by studying the number of intersections with a fixed...

video lecture

Chern classes of Schubert cells and varieties

March 30, 2015

June Huh

Chern-Schwartz-MacPherson class is a functorial Chern class defined for any algebraic variety. I will give a geometric proof of a positivity conjecture of Aluffi and Mihalcea that Chern classes of Schubert cells and varieties in Grassmannians are...

video lecture

Intelligent learning: similarity control and knowledge transfer

March 30, 2015

Vladimir Vapnik

During last fifty years a strong machine learning theory has been developed. This theory includes: 1. The necessary and sufficient conditions for consistency of learning processes. 2. The bounds on the rate of convergence which in general cannot be...

video lecture

Most odd degree hyperelliptic curves have only one rational point

March 26, 2015

Bjorn Poonen

We prove that the probability that a curve of the form $y^2 = f(x)$ over $\mathbb Q$ with $\deg f = 2g + 1$ has no rational point other than the point at infinity tends to 1 as $g$ tends to infinity. This is joint work with Michael Stoll.

video lecture

Framed motives of algebraic varieties (after V. Voevodsky)

March 25, 2015

Ivan Panin

This is joint work with G .Garkusha. Using the machinery of framed sheaves developed by Voevodsky, a triangulated category of framed motives is introduced and studied. To any smooth algebraic variety $X$, the framed motive $M_{fr}(X)$ is associated...

video lecture

The Radio Time Domain and the Murchison Widefield Array and Beyond

March 24, 2015

David Kaplan

Explorations of the radio sky in the time-domain are an exciting frontier in astrophysics, and one where new observational capabilities will open up new windows on the universe. As one of a new generation of widefield, low-frequency radio telescopes...