We prove that if every problem in NP has n^k-size circuits for a
fixed constant k, then for every NP-verifier and every yes-instance
x of length n for that verifier, the verifier's search space has a
witness for x that can be encoded with a circuit...
I will discuss an approach to the subconvexity problem for
L-functions based on period integral formulae and amplification. In
particular, I will describe work in progress with Ruixiang Zhang
that attempts to prove a subconvex bound for the central...
We propose a new second-order method for geodesically convex
optimization on the natural hyperbolic metric over positive
definite matrices. We apply it to solve the operator scaling
problem in time polynomial in the input size and logarithmic in
the...
Complexity of the geometry, randomness of the potential, and
many other irregularities of the system can cause powerful, albeit
quite different, manifestations of localization: a phenomenon of
confinement of waves, or eigenfunctions, to a small...
We propose a new second-order method for geodesically convex
optimization on the natural hyperbolic metric over positive
definite matrices. We apply it to solve the operator scaling
problem in time polynomial in the input size and logarithmic in
the...
A basic but difficult question in the analytic theory of
automorphic forms is: given a reductive group G and a
representation r of its L-group, how many automorphic
representations of bounded analytic conductor are there? In this
talk I will present...
The problem of bounding character twists of low-rank L-functions
has been attacked using a variety techniques, including delta
methods and analysis of period integral representations. I'll
discuss this problem, emphasizing joint work with Roman...
(joint w. Ben Bakker) Period spaces are quotients of period
domains by arithmetic groups that parametrize hodge structures.
These are typically complex-analytic orbifolds, but in most cases
cannot be equipped with an algebraic structure. As a...
Let F be a family of subsets over a domain X that is closed
under taking intersections. Such structures are abundant in various
fields of mathematics such as topology, algebra, analysis, and
more. In this talk we will view these objects through the...
Ribbon graphs capture the topology of open Riemann surfaces in
an elementary combinatorial form. One can hope this is the first
step toward a general theory for open symplectic manifolds such as
Stein manifolds. We will discuss progress toward such...
