Institut Henri Poincaré

Type:

Cours doctoraux
Site:

IHP
Date:

22/06/2011 - 09:00 - 17:30
Salle:

Amphithéâtre Darboux
Orateur:

TANNER Jared
Localisation:

Université d'Édimbourg
Localisation:

Royaume-Uni
Résumé:

Stochastic geometry and random matrix theory can be used to model and analyse the efficacy of a new paradigm in signal processing, compressed sensing. This new perspective shows that if a signal is sufficiently simple, it can be acquired at a rate proportional to its information content rather than the worst case rate dictated by a larger ambient space containing it. These lectures will show how this phenomenon can be modelled using stochastic geometry, and will also show how standard eigen-analysis in random matrix theory can give similar results.

Type:

Cours doctoraux
Site:

IHP
Date:

21/06/2011 - 09:00 - 17:30
Salle:

Amphithéâtre Darboux
Orateur:

TANNER Jared
Localisation:

Université d'Édimbourg
Localisation:

Royaume-Uni
Résumé:

Stochastic geometry and random matrix theory can be used to model and analyse the efficacy of a new paradigm in signal processing, compressed sensing. This new perspective shows that if a signal is sufficiently simple, it can be acquired at a rate proportional to its information content rather than the worst case rate dictated by a larger ambient space containing it. These lectures will show how this phenomenon can be modelled using stochastic geometry, and will also show how standard eigen-analysis in random matrix theory can give similar results.

Type:

Cours doctoraux
Site:

IHP
Date:

20/06/2011 - 09:00 - 17:30
Salle:

Amphithéâtre Darboux
Orateur:

TANNER Jared
Localisation:

Université d'Édimbourg
Localisation:

Royaume-Uni
Résumé:

Stochastic geometry and random matrix theory can be used to model and analyse the efficacy of a new paradigm in signal processing, compressed sensing. This new perspective shows that if a signal is sufficiently simple, it can be acquired at a rate proportional to its information content rather than the worst case rate dictated by a larger ambient space containing it. These lectures will show how this phenomenon can be modelled using stochastic geometry, and will also show how standard eigen-analysis in random matrix theory can give similar results.

Type:

Cours doctoraux
Site:

IHP
Date:

22/06/2011 - 09:00 - 17:30
Salle:

Amphithéâtre Darboux
Orateur:

VERSHYNIN Roman
Localisation:

Université du Michigan
Localisation:

États-Unis
Résumé:

This is a mini-course on basic non-asymptotic methods and concepts in random matrix theory. We will develop several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of these methods sprung off from the development of geometric functional analysis in the 1970-2000's. They have applications in several fields, most notably in theoretical computer science, statistics and signal processing. Two applications will be discussed: for the problem of estimating covariance matrices in statistics, and for validating probabilistic constructions of measurement matrices in compressed sensing.

Type:

Cours doctoraux
Site:

IHP
Date:

21/06/2011 - 09:00 - 17:30
Salle:

Amphithéâtre Darboux
Orateur:

VERSHYNIN Roman
Localisation:

Université du Michigan
Localisation:

États-Unis
Résumé:

This is a mini-course on basic non-asymptotic methods and concepts in random matrix theory. We will develop several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of these methods sprung off from the development of geometric functional analysis in the 1970-2000's. They have applications in several fields, most notably in theoretical computer science, statistics and signal processing. Two applications will be discussed: for the problem of estimating covariance matrices in statistics, and for validating probabilistic constructions of measurement matrices in compressed sensing.

Type:

Cours doctoraux
Site:

IHP
Date:

20/06/2011 - 09:00 - 17:30
Salle:

Amphithéâtre Darboux
Orateur:

VERSHYNIN Roman
Localisation:

Université du Michigan
Localisation:

États-Unis
Résumé:

This is a mini-course on basic non-asymptotic methods and concepts in random matrix theory. We will develop several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of these methods sprung off from the development of geometric functional analysis in the 1970-2000's. They have applications in several fields, most notably in theoretical computer science, statistics and signal processing. Two applications will be discussed: for the problem of estimating covariance matrices in statistics, and for validating probabilistic constructions of measurement matrices in compressed sensing.

Type:

Cours doctoraux
Site:

IHP
Date:

05/12/2011 - 09:00 - 12:30
Salle:

Salle 005
Orateur:

SCHOEN Richard
Localisation:

Université Stanford
Localisation:

États-Unis
Résumé:

This course will introduce the Einstein equations and describe some mathematical problems which arise in their study. We will focus on areas in which recent progress has been made.

Topics will include the Cauchy problem and the constraint equations. We will describe questions concerning the asymptotic behavior of solutions of the constraint equations and density theorems. These will elucidate the behavior of the energy and linear and angular momentum for asymptotically flat spacetimes. We will describe recent progress on mass/angular momentum inequalities.

We will also discuss questions relating to gravitational energy and positive energy theorems as well as notions of quasilocal mass. Some of the tools here include minimal hypersurface theory, inverse mean curvature flow, and the Dirac operator.

Type:

Cours doctoraux
Site:

IHP
Date:

06/12/2011 - 09:00 - 12:30
Salle:

Salle 201
Orateur:

SCHOEN Richard
Localisation:

Université Stanford
Localisation:

États-Unis
Résumé:

This course will introduce the Einstein equations and describe some mathematical problems which arise in their study. We will focus on areas in which recent progress has been made.

Topics will include the Cauchy problem and the constraint equations. We will describe questions concerning the asymptotic behavior of solutions of the constraint equations and density theorems. These will elucidate the behavior of the energy and linear and angular momentum for asymptotically flat spacetimes. We will describe recent progress on mass/angular momentum inequalities.

We will also discuss questions relating to gravitational energy and positive energy theorems as well as notions of quasilocal mass. Some of the tools here include minimal hypersurface theory, inverse mean curvature flow, and the Dirac operator.

Type:

Cours doctoraux
Site:

IHP
Date:

29/11/2011 - 09:00 - 12:30
Salle:

Salle 201
Orateur:

SCHOEN Richard
Localisation:

Université Stanford
Localisation:

États-Unis
Résumé:

This course will introduce the Einstein equations and describe some mathematical problems which arise in their study. We will focus on areas in which recent progress has been made.

Topics will include the Cauchy problem and the constraint equations. We will describe questions concerning the asymptotic behavior of solutions of the constraint equations and density theorems. These will elucidate the behavior of the energy and linear and angular momentum for asymptotically flat spacetimes. We will describe recent progress on mass/angular momentum inequalities.

We will also discuss questions relating to gravitational energy and positive energy theorems as well as notions of quasilocal mass. Some of the tools here include minimal hypersurface theory, inverse mean curvature flow, and the Dirac operator.

Type:

Cours doctoraux
Site:

IHP
Date:

28/11/2011 - 09:00 - 12:30
Salle:

Salle 201
Orateur:

SCHOEN Richard
Localisation:

Université Stanford
Localisation:

États-Unis
Résumé: