Video Lectures

The trace formula has been the most powerful and mainstream tool in automorphic forms for proving instances of Langlands functoriality, including character relations. Its generalization, the relative trace formula, has also been used to prove...

I will survey some of the basic approaches to derandomizing Probabilistic Logspace computations, including the "classical" Nisan, Impagliazzo-Nisan-Widgerson and Reingold-Raz generators, the Saks-Zhou algorithm and some more recent approaches. We'll...

Fundamental questions in basic and applied ecology alike involve complex adaptive systems, in which localized interactions among individual agents give rise to emergent patterns that feed back to affect individual behavior. In such systems, a...

Polar codes have recently emerged as a new class of low-complexity codes achieving Shannon capacity. This talk introduces polar codes with emphasis on the probabilistic phenomenon underlying the code construction. New results and connections to...

I will present new results concerning the approximation of the BV-norm by nonlocal, nonconvex, functionals. The original motivation comes from Image Processing. Numerous problems remain open. The talk is based on a joint work with H.-M. Nguyen.