From the very beginnings of cinematography, themes from the
ancient world and the Bible have provided directors and
screenwriters with inspiration. The representation of antiquity in
the movies, and more generally in pop culture, is now a...
This is the second of two talks in which the speaker will
discuss the development of the theory of Toeplitz matrices and
determinants in response to questions arising in the analysis of
the Ising model of statistical mechanics. The first talk
will...
A linear property of Banach spaces is called "local" if it
depends on finite number of vectors and is invariant under
renorming (i.e., distorting the norm by a finite factor). A famous
theorem of Ribe states that local properties are invariant
under...
This is the first of two talks in which the speaker will discuss
the development of the theory of Toeplitz matrices and determinants
in response to questions arising in the analysis of the Ising model
of statistical mechanics. The first talk will be...
We study the problem of constructing extractors for independent
weak random sources. The probabilistic method shows that such an
extractor exists for two sources on n bits with min-entropy k >=
2 log n. On the other hand, explicit constructions are...
Abstract:
Associated to an abelian variety A/K is a Galois representation
which describes the action of the absolute Galois group of K on the
torsion points of A. In this talk, we shall describe how large the
image of this representation can be (in...
We develop a simple geometric variant of the
Kabatiansky-Levenshtein approach to proving sphere packing density
bounds. This variant gives a small improvement to the best bounds
known in Euclidean space (from 1978) and an exponential improvement
in...
Several examples of Hamiltonian evolution equations for systems
with infinitely many degrees of freedom are presented. It is
sketched how these equations can be derived from some underlying
quantum dynamics ("mean-field limit") and what kind of...
