Video Lectures

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...

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...

We study some problems relating to polynomials evaluated either at random Gaussian or random Bernoulli inputs. We present some new work on a structure theorem for degree-d polynomials with Gaussian inputs. In particular, if p is a given degree-d...

We propose an “analytical” framework for studying parallel repetitions of one-round two-prover games. We define a new relaxation of the value of a game, val+, and prove that it is both multiplicative and a good approximation for the true value of...

To apply the technique of virtual fundamental cycle (chain) in the study of pseudo-holomorphic curve, we need to construct certain structure, which we call Kuranishi strucuture, on its moduli space. In this talk I want to review certain points of...