Video Lectures

In 2000 Eliashberg-Polterovich introduced the concept of positivity in contact geometry. The notion of a positive loop of contactomorphisms is central. A question of Eliashberg-Polterovich is whether $C^0$-small positive loops exist. We give a...

We discuss our results on global existence and convergence of solutions to the gradient flow equation for the Yang-Mills energy functional over a closed, four-dimensional, Riemannian manifolds: If the initial connection is close enough to a minimum...

Stochastic quantization equations are evolutionary PDEs driven by space-time white noises. They are proposed by physicists in the 80s as the natural dynamics associated to the (Euclidean) quantum field theories. We will discuss the recent progress...

I will talk about convex-cocompact representations of finitely generated free group $F_g$ into $\mathrm{PSL}(2,\mathbb C)$. First I will talk about Schottky criterion. There are many ways of characterizes Schottky group. In particular, convex hull...

I want to sketch some algebraic and geometric tools to solve a variety of extremal problems surrounding Minkowski sums of polytopes and colorful simplicial depth.

We study the two-party communication complexity of the geometric problem of finding an approximate Brouwer fixed-point of a composition of two Lipschitz functions $g \circ f$, where Alice knows $f$ and Bob knows $g$. We prove an essentially tight...

Join Matias Zaldarriaga, Professor in the School of Natural Sciences, Scott Tremaine, Richard Black Professor in the School, and Members Doron Kushnir and Nadia Zakamska for a discussion of the recent Laser Interferometer Gravitational-Wave...

In joint work with Emmanuel Kowalski and Philippe Michel, we prove two different estimates on sums of coefficients of modular forms---one related to L-functions and another to the level of distribution. A key step in the argument is a careful...

I'll outline the construction and computation of a Floer homology theory for contact manifolds which are prequantization spaces over monotone symplectic manifolds, and of the spectral invariants resulting therefrom, and present some applications...

While this lecture is a continuation of the lecture from last Tuesday, I will make it self contained. The main object of study of this talk are matrices whose entries are linear forms in a set of formal variables (over some field). The main problem...