I will describe some recent results and problems regarding
influence of sets of variables on Boolean functions: In 1989 Benny
Chor conjectured that a balanced Boolean function with n variables
has a subset S of size 0.4n with influence (1-c^n) where...
We will discuss recent work on wave evolutions for large data.
Particular emphasis will be placed on concentration compactness
ideas. Amongst others, we will describe a result for wave equations
from R^3 minus the unit ball into the sphere S^3 where...
Application of Plancherel's theorem to integral kernels
approximating compact period functionals yields estimates on
(global) automorphic Levi-Sobolev norms of the functionals. The
utility of this viewpoint can be illustrated in reconsideration
of...
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...
