Video Lectures

Let \(R={\cal O}_{{\bf C},0}\) be the ring of power series convergent in a neighborhood of zero in the complex plane. Every scheme \(\cal X\) of finite type over \(R\) defines a complex analytic space \({\cal X}^h\) over an open disc \(D\) of small...

The stochastic Burgers equation (equivalent to the one-dimensional KPZ equation) is a hyperbolic conservation law with random currents. In applications, one often has to deal with several conservation laws, a little explored case. We discuss...

In several naturally occurring (infinite) point processes, we show that the number (and other statistical properties) of the points inside a finite domain are determined, almost surely, by the point configuration outside the domain. This curious...

Robbert Dijkgraaf moderates a panel of 6 Nobel Laureates on the value of fundamental science and curiosity driven research at the 2013 Nobel Week Dialogue. Video reproduced with permission by Nobel Week Dialogue and Nobel Media AB.

In this lecture, Alexander Nagel, Professor of Fine Arts at the Institute of Fine Arts at New York University, illustrates some ways in which art produced during the Renaissance period points ­eastward towards Constantinople, towards the Holy Land...

I describe recent results on spiked covariance matrices, which model multivariate data containing nontrivial correlations. In principal components analysis, one extracts the leading contribution to the covariance by analysing the top eigenvalues and...

Feynman categories are a new universal categorical framework for generalizing operads, modular operads and twisted modular operads. The latter two appear prominently in Gromov-Witten theory and in string field theory respectively. Feynman categories...

We discuss two random decreasing sequences of continuous functions in two variables, and how they arise as the scaling limit from corners of a (real / complex) Wigner matrix undergoing stochastic evolution. The restriction of the second one to...