Video Lectures

In this talk I will describe nondeterministic reductions which yield new direct product theorems (DPTs) for Boolean circuits. In our theorems one assumes that a function F is "mildly hard" against *nondeterministic* circuits of some size s(n) , and...

In many distributed systems, the cost of computation is dominated by the cost of communication between the machines participating in the computation. Communication complexity is therefore a very useful tool in understanding distributed computation...

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...

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...

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).

Informally, uncertainty principle says that function and its Fourier transform can not be both concentrated. Uncertainty principle has a lot of applications in areas like compressed sensing, error correcting codes, number theory and many others. In...