Video Lectures

This is the third talk in a series of three talks on the derived Satake equivalence. I will give an overview of the article of Bezrukavnikov and Finkelberg which explains how the equivariant derived category of the affine Grassmannian can be...

We show that if G=⟨S|E⟩ is a discrete group with Property (T) then E, as a system of equations over S, is not stable (under a mild condition). That is, E has approximate solutions in symmetric groups Sym(n), n≥1, that are far from every solution in...

Sometimes, it is possible to represent a complicated polytope as a projection of a much simpler polytope. To quantify this phenomenon, the extension complexity of a polytope P is defined to be the minimum number of facets in a (possibly higher...

We will briefly review Kolmogorov’s (41) theory of homogeneous turbulence and Onsager’s (49) conjecture that in 3-dimensional turbulent flows energy dissipation might exist even in the limit of vanishing viscosity. Although over the past 60 years...

You can make a paper Moebius band by starting with a 1 by L rectangle, giving it a twist, and then gluing the ends together. The question is: How short can you make L and still succeed in making the thing? This question goes back to B. Halpern and C...

We introduce two new notions for polynomials associated with discrete set-valued probability distributions. These notions generalize well-studied properties like real-stability and log-concavity, but unlike them robustly degrade under a number of...

We first describe mathematical foundation of DSGRN (Dynamic Signatures Generated by Regulatory Networks), an approach that provides a queryable description of global dynamics of a network over its entire param- eter space. We describe a connection...

Viterbo conjectured that a normalized symplectic capacity, on convex domains of a given volume, is maximized for the ball. A stronger version of this conjecture asserts that all normalized symplectic capacities agree on convex domains. Since...

A classical result identifies holomorphic modular forms with highest weight vectors of certain representations of SL2(ℝ). We study locally analytic vectors of the (p-adically) completed cohomology of modular curves and prove a p-adic analogue of...