Video Lectures

A continuous representation of a profinite group induces a continuous pseudorepresentation, where a pseudorepresentation is the data of the
characteristic polynomial coefficients. We discuss the geometry of the resulting map from the moduli formal...

Politics is not merely a series of policy battles, but an ongoing struggle for the primacy of our favored understandings about both how the world is and how it ought to be. For a social movement to be successful, it must win discrete policy battles, but, more importantly, re-write the political field in its own favor. Social movements achieve lasting success not primarily through pursuing political changes, but by changing politics itself.

I present a new, fully anisotropic, criterion for formation of trapped surfaces in vacuum obtained in collaboration with J. Luk and I. Rodnianski. We provide conditions on null data, concentrated in a neighborhood of a short null geodesic segment...

We study algorithms for combinatorial market design problems, where a collection of objects are priced and sold to potential buyers subject to equilibrium constraints. We introduce the notion of a combinatorial Walrasian equilibium (CWE) as a...

We present practically efficient methods for proving correctness of announced results of a computation while keeping input and intermediate values information theoretically secret. These methods are applied to solve the long standing problem of...

A large class of one dimensional stochastic particle systems are predicted to share the same universal long-time/large-scale behavior. By studying certain integrable models within this (Kardar-Parisi-Zhang) universality class we access what should...

Cellular telephones, GPS, radar imaging, and most other modern wireless systems would not exist without the sophisticated mathematical and digital techniques that are used to encode and decode their messages. These “spread spectrum” methods, under...

I will discuss recent work on the global stability of the Euler-Maxwell equations in 3D (joint work with Guo and Pausader), and of the gravity water-wave system in 2D (joint work with Pusateri).

We study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a...