Video Lectures

In the optimal transport problem, it is well-known that the geometry of the target domain plays a crucial role in the regularity of the optimal transport. In the quadratic cost case, for instance, Caffarelli showed that having a convex target domain...

I'll show a graphical user interface I wrote which explores the problem of inscribing rectangles in Jordan loops. The motivation behind this is the notorious Square Peg Conjecture of Toeplitz, from 1911.

I did not manage to solve this problem, but I...

A fundamental task in (unsupervised) analysis of data is to detect and estimate interesting "structure" hidden in it. In low dimensions, this task has been explored for over 100 years with dozens of developed methods. In this talk I'll focus on...

The choiceless computation model of Blass, Gurevich and Shelah (1999, 2002) is an algorithmic framework for computing isomorphism-invariant properties of unordered structures. Machines in this model have the power of parallel execution, but lack...

We consider Laplace eigenfunctions of a metric graph satisfying Neumann-Kirchhoff conditions on every vertex. The nodal count of a given eigenfunction is the number of points at which it vanishes. The nodal count of the n-th eigenfunction was shown...

This talk is about qualitative properties of the underlying scheme of Rapoport-Zink formal moduli spaces of p-divisible groups, resp. Shtukas. We single out those cases when the dimension of this underlying scheme is zero, resp. those where the...

Most people interact with machine learning systems on a daily basis. Such interactions often happen in strategic environments where people have incentives to manipulate the learning algorithms. As machine learning plays a more prominent role in our...

The first lecture in this series is an introduction to the theory of asymptotic spectra. This theory describes asymptotic behavior of basic objects in mathematics like graphs and tensors. Example applications that we will see are the matrix...

In various applications, one is given the advice or predictions of several classifiers of unknown reliability, over multiple questions or queries. This scenario is different from standard supervised learning where classifier accuracy can be assessed...

In a recent result, Buckmaster and Vicol proved non-uniqueness of weak solutions to the Navier-Stokes equations which have bounded kinetic energy and integrable vorticity.

We discuss the existence of such solutions, which in addition are regular...