A general algebraic formalism for the mathematical modeling of
physical systems is sketched. This formalism is sufficiently
general to encompass classical and quantum-mechanical models. It is
then explained in which way quantum theory differs in an...
In this talk we will discuss information complexity -- a measure
of the amount of information Alice and Bob need to exchange to
solve a problem over distributed inputs. We will present an
information-theoretically optimal protocol for computing the...
For all practical purposes, the Micali-Vazirani algorithm,
discovered in 1980, is still the most efficient known maximum
matching algorithm (for very dense graphs, slight asymptotic
improvement can be obtained using fast matrix
multiplication)...
The PCP theorem (Arora et. al., J. ACM 45(1,3)) asserts the
existence of proofs that can be verified by reading a very small
part of the proof. Since the discovery of the theorem, there has
been a considerable work on improving the theorem in terms...
We consider Galois cohomology groups over function fields F of
curves that are defined over a complete discretely valued
field.
Motivated by work of Kato and others for n=3, we show that
local-global principles hold for
$H^n(F, Z/mZ(n-1))$ for all...
This is from joint works with D. Knopf and I. M. Sigal. In this
talk I will present a new strategy in studying neckpinching of mean
curvature flow. Different from previous results, we do not use
backward heat kernel, entropy estimates or subsequent...
Often mathematicians refer to a "beautiful" result or a
"beautiful" proof. In this special lecture, Enrico Bombieri,
Professor Emeritus in the School of Mathematics, addresses the
question, "What is beauty in mathematics?"
A `toy model' for studying the probabilistic distribution of
nodal curves of eigenfunctions of linear operators arises from the
Laplacian on the standard real 2-torus. Here the eigenvalues are
associate to integers m that are sum of two squares...
