This is joint work with A. B. Goncharov. To any convex integer
polygon we associate a Poisson variety, which is essentially the
moduli space of connections on line bundles on (certain) bipartite
graphs on a torus. There is an underlying integrable...
We review the well known microscopic correspondence between
random zeros of the Riemann zeta-function and the eigenvalues of
random matrices, and discuss evidence that this correspondence
extends to larger mesoscopic collections of zeros or...
Thanks to the work of Katz and Sarnak on L-functions over
function fields, we know that the Frobenius classes associated to
L-functions of hyperelliptic curves over a finite field with $q$
elements, $F_{q}$, becomes equidistributed in the unitary...
A number is said to be $y$-smooth if all of its prime factors
are less than $y$. Such numbers appear in many places throughout
analytic and combinatorial number theory, and much work has been
done to investigate their distribution.
I will try to...
Consider a group of measure preserving transformations acting on
a probability space. The limiting behavior of the nonconventional
ergodic averages associated with this action has been the subject
of much attention since the work of Furstenberg on...
Locally decodable codes (LDCs) are error-correcting codes that
allow for highly-efficient recovery of "pieces" of information even
after arbitrary corruption of a codeword. Locally testable codes
(LTCs) are those that allow for highly-efficient...