School of Mathematics

The Ribe Program

Manor Mendel
The Open University of Israel; Member, School of Mathematics
January 29, 2013

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 (non linear) uniform-homeomorphisms, suggesting that local properties should have purely metric characterizations.
The Ribe program attempts to uncover explicit metric characterizations of local properties, and study them in the context of metric spaces. More broadly it attempts to apply ideas from Banach

Toeplitz Matrices and Determinants Under the Impetus of the Ising Model

Percy Deift
Courant Institute, NYU
January 29, 2013

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 be largely historical and the second will describe the state of the art today, including recent results of the speaker and his colleagues Alexander Its and Igor Krasovsky.

Toeplitz Matrices and Determinants Under the Impetus of the Ising Model

Percy Deift
Courant Institute, NYU
January 28, 2013

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 largely historical and the second will describe the state of the art today, including recent results of the speaker and his colleagues Alexander Its and Igor Krasovsky.

Abelian varieties with maximal Galois action on their torsion points

David Zywina
January 24, 2013

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 terms of a number field K and the dimension of A). We achieve this by considering abelian varieties in families and then using a special variant of Hilbert's irreducibility theorem. Some results of Serre on the mod ell Galois image will also be reviewed. (This is joint work with David Zureick-Brown)

Sparsity Lower Bounds for Dimensionality Reducing Maps

Jelani Nelson
Member, School of Mathematics
January 22, 2013

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 up to a log(1/eps) factor.
(2) RIP_2 matrices preserving k-space vectors in R^n with the optimal number of rows must be dense as long as k < n / polylog(n).