Shannon's notion of entropy measures the amount of "randomness"
in a process. However, to an algorithm with bounded resources, the
amount of randomness can appear to be very different from the
Shannon entropy. Indeed, various measures of...
I will report on some recent work on multiple zeta values. I
will sketch the definition of motivic multiple zeta values, which
can be viewed as a prototype of a Galois theory for certain
transcendental numbers, and then explain how they were used...
One of the principal questions about L-functions is the size of
their critical values. In this talk, we will present a new
subconvexity bound for the central value of a Dirichlet L-function
of a character to a prime power modulus, which breaks a...
A property of finite graphs is called nondeterministically
testable if it has a "certificate'' such that once the certificate
is specified, its correctness can be verified by random local
testing. In this talk we consider certificates that consist...
The goal of the Balanced Separator problem is to find a balanced
cut in a given graph G(V,E), while minimizing the number of edges
that cross the cut. It is a fundamental problem with applications
in clustering, image segmentation, community...
We study the list-decodability of multiplicity codes.
These codes, which are based on evaluations of high-degree
polynomials and their derivatives, have rate approaching 1 while
simultaneously allowing for sublinear-time error-correction. In
this...
Heegaard Floer homology groups were recently introduced by
Ozsvath and Szabo to study properties of 3-manifolds and knots in
them. The definition of the invariants rests on delicate
holomorphic geometry, making the actual computations
cumbersome...
Heegaard Floer homology groups were recently introduced by
Ozsvath and Szabo to study properties of 3-manifolds and knots in
them. The definition of the invariants rests on delicate
holomorphic geometry, making the actual computations
cumbersome...
