Video Lectures

In a profoundly influential 1948 paper, Claude Shannon defined the entropy function H, and showed that the capacity of a symmetric binary channel with noise rate (bit flip rate) eps is 1−H(eps). This means that one can reliably communicate n bits by...

A widely studied model from statistical physics consists of many (one-dimensional) Brownian motions interacting through a pair potential. The large scale behavior of this model has has been investigated by Varadhan, Yau, and others in the 90's. As a...

Machine learning is often employed as one step in a larger application, serving to perform information extraction or data mining for example. The rules obtained by such learning are then used as inputs to a further analysis. As a consequence of the...

One of the most amazing things we discovered in science is that everything is made of small particles. It's the properties of these molecules, atoms, nuclei, and elementary particles that allow us to answer ­simple questions like: why is grass green...

I will report on joint work with Nick Sheridan concerning structural aspects of mirror symmetry for Calabi-Yau manifolds. We show (i) that Kontsevich's homological mirror symmetry (HMS) conjecture is a consequence of a fragment of the same...

Let \(k\) be an algebraically closed field and let \(c:C\rightarrow X\times X\) be a correspondence. Let \(\ell \) be a prime invertible in \(k\) and let \(K\in D^b_c(X, \overline {\mathbb Q}_\ell )\) be a complex. An action of \(c\) on \(K\) is by...

Historians have debated for centuries the magnitude, nature, and impact of population movements from the borders of the Roman Empire into its heart between the fourth and seventh centuries. In recent years, geneticists have begun to attempt to...