We study the Lyapunov exponent in disordered quantum field
theories. Generically the Lyapunov exponent can only be computed in
isolated CFTs, and little is known about the way in which chaos
grows as we deform the theory away from weak coupling. In...
What does the spectrum of a random matrix look like when we make
no assumption whatsoever about the covariance pattern of its
entries? It may appear hopeless that anything useful can be
said at this level of generality. Nonetheless, a widely used...
We study CM cycles on Kuga-Sato varieties over X(N) via theta
lifting and relative trace formula. Our first result is the
modularity of CM cycles, in the sense that the Hecke modules they
generate are semisimple whose irreducible components are...
In this talk I will discuss two undetected populations of black
holes. In the faraway Universe, the first lensed z > 6 quasar
(J0439+1634) was recently discovered. We predicted that the
observed population of quasars should contain many mildly...
I'll describe a method for analyzing the first-order theory of
an arithmetic group using its congruence quotients. When this
method works, it gives a strong form of first-order rigidity
together with a complete description of the collection of...
The query model is one of the most basic computational
models. In contrast to the Turing machine model, fundamental
questions regarding the power of randomness and quantum computing
are relatively well-understood. For example, it is
well-known...
