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

  Spacetime wormholes have played an important role in recent progress in black hole physics. However, in the context of AdS/CFT, these wormholes lead to a basic puzzle: the "factorization problem", introduced by Maldacena and Maoz. In this talk we...

We will give an explicit construction and description of a supercuspidal local Langlands correspondence for any p-adic group G that splits over a tame extension, provided p does not divide the order of the Weyl group. This construction matches any...

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...