Conferences in June 2013

In June 2013 there will be one conference and two mini-workshops. The main subjects of interest in this second series are large quantum systems in general.

 

June 14, 2013: MINI-WORKSHOP
"The mathematics of interacting quantum systems in a random environment"
Organizers: Eric Cancès (ENPC, Paris), Frédéric Klopp (Paris 6).

List of invited speakers:
Xavier Blanc (Paris, France), Robert Sims (Tucson, Arizona, USA), Simone Warzel (Munich, Germany), Jakob Yngvason (Vienna, Austria), Valentin Zagrebnov (Marseille, France)

 See the detailed program

June 17 - June 21, 2013: CONFERENCE
"Mathematical properties of large quantum systems"
Organizers: Maria J. Esteban (CNRS), Mathieu Lewin (CNRS), Robert Seiringer (IST, Vienna), Jan Philip Solovej (Copenhagen).

List of invited speakers:
Volker Bach (Braunschweig, Germany), Rafael Benguria (Santiago, Chile), Yvan Castin (Paris, France), Søren Fournais (Aarhus, Denmark), Alessandro Giuliani (Roma, Italy), Philippe Gravejat (Paris, France), Manoussos Grillakis (Univ. Maryland, USA), Markus Holzmann (Grenoble, France), Vojkan Jaksic (Montréal, Canada), Isaac H. Kim (Caltech, USA), Salma Lahbabi (Cergy-Pontoise, France), Ari Laptev (London, UK), Enno Lenzmann (Basel, Switzerland), Elliott H. Lieb (Princeton, USA), Michael Loss (Atlanta, USA), Douglas Lundholm (Paris, France), Nick Manton (Cambridge, UK), Phan Thanh Nam (Cergy-Pontoise, France), Thomas Østergaard Sørensen (Munich, Germany), Nicolas Rougerie (Grenoble, France), Benjamin Schlein (Bonn, Germany), Sylvia Serfaty (Paris, France), Daniel Ueltschi (Warwick, UK), Maria Vozmediano (Madrid, Spain), Michael Weinstein (New York, USA), Jun Yin (Madison, USA)

See the detailed program

See some pictures


 
June 24, 2013: MINI-WORKSHOP
"Mathematical and numerical challenges in quantum chemistry"
Organizers:  Claude Le Bris (ENPC, Paris), Christian Lubich (Tuebingen).

List of invited speakers:
Michel Caffarel (Toulouse, France), Eric Cancès (Paris, France), Carlos Garcia-Cervera (Santa Barbara, USA), Simen Kvaal (Oslo, Norway), Reinhold Schneider (Berlin, Germany), Harry Yserentant (Berlin, Germany)

See the detailed program


June 25-26, 2013: SATELLITE MEETING at the University of Cergy-Pontoise
"Entropy in Quantum Mechanics: Recent Advances"
Organizers: Laurent Bruneau (Cergy), Vojkan Jaksic (Montréal), Flora Koukiou (Cergy), Mathieu Lewin (Cergy) & Robert Seiringer (Vienna)
Read more on the website of the University of Cergy-Pontoise

 

There is no conference fee. However please register on the IHP website.

 

*to be confirmed

Seminars

There are two seminars during the trimester at the IHP:


On April 15, May 13 and June 10, the seminar will merge with the Seminar "Spectral Problems in Mathematical Physics", organized by Clotilde Fermanian and Stéphane Nonnenmacher.

 

Overview

Here is the whole scientific program of the trimester at a glance.

 

 

Lectures for students

There were 2 courses for students (master or PhD), of 8h each, during the trimester at IHP. The courses were given in english.

Click here to see the detailed schedule for the lectures in June
Click here to see the videos of the lectures

Lecture 1: Interpolation inequalities and applications to nonlinear PDE
Enno Lenzmann (Basel, Switzerland)

Duration: 8h between June 3rd and June 13th, 2013

Summary: Interpolation inequalities and their optimizers play a central role in the analysis of many nonlinear evolution problems (e.g. nonlinear Schrödinger and wave equations, water wave problems etc.). The present course will be divided into three main sections as follows. In the first (introductory) part of this course, we will review some "classical" results and techniques to show existence, symmetry and uniqueness for optimizers for Sobolev and Hardy-Littlewood-Sobolev inequalities. In the second part of this course, we discuss some recent approaches to show uniqueness and symmetry of optimizers with particular emphasis on interpolation estimates involving the fractional Laplacian. In the final part of the course, we focus on various applications to nonlinear evolution PDE.
 
Prerequisites of the course: a good knowledge of advanced analysis (e.g. on the level of the Lieb & Loss textbook "Analysis"). Some further knowledge of PDE and variational calculus is desirable but not mandatory.

 

Lecture 2: Operators and their perturbations
Jan Derezinski (Warsaw, Poland)

Duration: 8h between June 3rd and June 13th, 2013

Summary: The main purpose of the course is to develop general theory of perturbations of linear operators on Hilbert space, with the emphasis on Schrödinger operators. Many concrete examples will be described in detail. List of subject that will be (partially) covered:

1) Reminder of basic spectral theory

- Unbounded operators
- Closed operators
- Spectrum
- Relative boundedness
- Pseudoresolvents
- Unbounded operators on Hilbert spaces
- (Essential) self-adjointness
- Scale of Hilbert spaces
- Closed and closable positive forms
- Friedrichs extensions

2) Reminder of basic harmonic analysis and its applications

- Young inequality
- Fourier transformation
- Sobolev inequalities
- Self-adjointness of Schrödinger operators
- Self-adjointness of many-body Schrödinger operators

3) Momentum and Laplacian on the line

- Momentum on half-line
- Momentum on an interval
- Laplacian on half-line
- Laplacian on an interval

4) Orthogonal polynomials

- Orthogonal polynomials in  weighted L2 spaces
- Self-adjointness of Sturm-Liouville operators
- Classical orthogonal polynomials as eigenvectors of certain Sturn-Liouville operators
- Hermite polynomials
- Laguerre polynomials
- Jacobi polynomials

5) Finite rank perturbations and their renormalization

- Aronszajn-Donoghue Hamiltonians
- Delta potentials
- Friedrichs Hamiltonians
- Bound states and resonances of Friedrichs Hamiltonians
- Exponential decay from a unitary dynamics

6) Potential 1/|x|²

- Hardy inequality
- Modified Bessel  equation
- Bessel equation
- Operator -xx+(m²-1/4)/x2