Video Lectures

The Langlands and Fontaine–Mazur conjectures in number theory describe when an automorphic representation f arises geometrically, meaning that there is a smooth projective variety X, or more generally a Chow motive M in the cohomology of X, such...

My talk will aim to be a friendly introduction for condensed matter friends, mathematicians, and QFT theorists alike --- I shall quickly review and warm up the use of higher symmetries and anomalies of gauge theories and condensed matter systems...

I will describe joint work with Boris Solomyak, in which we show that the stationary (Furstenberg) measure on the projective line associated to 2x2 random matrix products has the "correct" dimension (entropy / Lyapunov exponent) provided that the...

In many-body chaotic systems, the size of an operator generically grows in Heisenberg evolution, and is measured by out-of-time-ordered four-point functions. However, these only provide a coarse probe of the full underlying operator growth structure...

Deligne's "Weil II" paper includes a far-reaching conjecture to the effect that for a smooth variety on a finite field of characteristic p, for any prime l distinct from p, l-adic representations of the etale fundamental group do not occur in...