# Video Lectures

High-precision astrometric data from space observatories, such as the Hubble Space Telescope (HST) and Gaia, are revolutionizing our ability to study the Local Group. 6D phase space measurements (3-dimensional position and velocity) now make it...

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...

Debris disks are signposts of mature planetary systems, and resolved images of dust grains act like test particles that trace the dynamics of embedded planets. I will describe ongoing efforts with the Atacama Large Millimeter/Submillimeter...

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 show that a naïve application of the quantum extremal surface (QES) prescription can lead to paradoxical results and must be corrected at leading order. The corrections arise when there is a second QES (with strictly larger generalized entropy at...

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...

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...