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...
Abstract:
We give near-tight lower bounds for the sparsity required in
several dimensionality reducing linear maps. In particular, we
show:
(1) The sparsity achieved by [Kane-Nelson, SODA 2012] in the sparse
Johnson-Lindenstrauss lemma is optimal...
