Lun. 03 | Mar. 04 | Mer. 05 | Jeu. 06 | Ven. 07 | |
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17:00 - 18:15 (1h15)
Accueil au centre
Accueil au centre
18:15 - 18:30 (15min)
Discours bienvenue
Discours de bienvenue
18:30 - 19:30 (1h)
Bernard Helffer ----------------------- On Courant and Pleijel theorems for sub-Riemannian Laplacians.
We are interested in the number of nodal domains of eigenfunctions of sub-Laplacians on sub-Riemannian manifolds. Specifically, we investigate the validity of Pleijel's theorem, which states that, as soon as the dimension is strictly larger than 1, the number of nodal domains of an eigenfunction corresponding to the k-th eigenvalue is strictly (and uniformly, in a certain sense) smaller than k for large k. In the first part of the talk we reduce this question from the case of general sub-Riemannian manifolds to that of nilpotent groups. In the second part, we analyze in detail the case where the nilpotent group is a Heisenberg group times a Euclidean space. Along the way we improve known bounds on the optimal constants in the Faber--Krahn and isoperimetric inequalities on these groups. This is a joint work with Rupert Frank (LMU München)
19:30 - 21:00 (1h30)
Dîner
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9:00 - 10:30 (1h30)
Patrick Gérard -------------------- Integrable equations of Benjamin-Ono type
In this mini-course, I will study two integrable
nonlinear dispersive equations on the line : the Benjamin-Ono equation
and the more recently introduced Calogero-Moser derivative
nonlinear Schrödinger equation.
The following topics will be discussed.
1. Local wellposedness in Sobolev spaces, Lax pair, explicit formulae.
2. Conservation laws and global wellposedness.
3. Traveling waves and multi-solitons.
4. Zero-dispersion limit.
10:30 - 11:00 (30min)
Pause café
11:00 - 12:00 (1h)
Pierre Germain ----------------------- TBA
Pierre Germain
12:15 - 14:00 (1h45)
Déjeuner
15:00 - 16:00 (1h)
Ewelina Zatorska ----------------------- TBA
Ewelina Zatorska
16:00 - 16:30 (30min)
Pause café
16:30 - 17:30 (1h)
Kevin Le Balc'h ----------------------- TBA
Kevin Le Balc'h
17:30 - 18:30 (1h)
Grégory Faye ----------------------- The local limit theorem for complex valued sequences: the parabolic case.
We give a complete expansion, at any accuracy order, for the iterated convolution of a complex valued integrable sequence in one space dimension. The remainders are estimated sharply with generalized Gaussian bounds. The result applies in probability theory for random walks as well as in numerical analysis for studying the large time behavior of numerical schemes. This is joint work with Jean-François Coulombel.
18:30 - 19:30 (1h)
Apéritif spécial 50 ans
19:30 - 21:00 (1h30)
Dîner
|
9:00 - 10:30 (1h30)
Patrick Gérard -------------------- Integrable equations of Benjamin-Ono type
In this mini-course, I will study two integrable
nonlinear dispersive equations on the line : the Benjamin-Ono equation
and the more recently introduced Calogero-Moser derivative
nonlinear Schrödinger equation.
The following topics will be discussed.
1. Local wellposedness in Sobolev spaces, Lax pair, explicit formulae.
2. Conservation laws and global wellposedness.
3. Traveling waves and multi-solitons.
4. Zero-dispersion limit.
10:30 - 11:00 (30min)
Pause café
11:00 - 12:00 (1h)
Yannick Bonthonneau ----------------------- TBA
Yannick Bonthonneau
12:15 - 13:30 (1h15)
Déjeuner
13:30 - 17:00 (3h30)
Visite du laboratoire souterrain de Modane
Visite du laboratoire souterrain de Modane
19:30 - 21:00 (1h30)
Dîner
|
9:00 - 10:30 (1h30)
Patrick Gérard -------------------- Integrable equations of Benjamin-Ono type
In this mini-course, I will study two integrable
nonlinear dispersive equations on the line : the Benjamin-Ono equation
and the more recently introduced Calogero-Moser derivative
nonlinear Schrödinger equation.
The following topics will be discussed.
1. Local wellposedness in Sobolev spaces, Lax pair, explicit formulae.
2. Conservation laws and global wellposedness.
3. Traveling waves and multi-solitons.
4. Zero-dispersion limit.
10:30 - 11:00 (30min)
Pause café
11:00 - 12:00 (1h)
Mikaela Iacobelli -------------------- Stability and singular limits in plasma physics.
In this talk, we will present two kinetic models that are used to describe the evolution of charged particles in plasmas: the Vlasov-Poisson system and the Vlasov-Poisson system with massless electrons. These systems model respectively the evolution of electrons, and ions in a plasma. We will discuss the well-posedness of these systems, the stability of solutions, and their behavior under singular limits. Finally, we will introduce a new class of Wasserstein-type distances specifically designed to tackle stability questions for kinetic equations.
12:15 - 14:00 (1h45)
Déjeuner
15:00 - 16:00 (1h)
Alberto Enciso ----------------------- TBA
Alberto Enciso
16:00 - 16:30 (30min)
Pause café
16:30 - 17:30 (1h)
Valeria Banica ----------------------- TBA
Valeria Banica
17:30 - 18:30 (1h)
Nicolas Camps ----------------------- TBA
Nicolas Camps
19:30 - 21:00 (1h30)
Dîner spécial : fondue
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9:00 - 10:30 (1h30)
Patrick Gérard -------------------- Integrable equations of Benjamin-Ono type
In this mini-course, I will study two integrable
nonlinear dispersive equations on the line : the Benjamin-Ono equation
and the more recently introduced Calogero-Moser derivative
nonlinear Schrödinger equation.
The following topics will be discussed.
1. Local wellposedness in Sobolev spaces, Lax pair, explicit formulae.
2. Conservation laws and global wellposedness.
3. Traveling waves and multi-solitons.
4. Zero-dispersion limit.
10:30 - 11:00 (30min)
Pause café
11:00 - 12:00 (1h)
Yvan Martel -------------------- Asymptotic stability of small solitary waves for the one-dimensional cubic-quintic Schrödinger equation with an internal mode.
I will present a result concerning the asymptotic stability of small solitary waves for the one-dimensional Schrödinger equation with a cubic-quintic, focusing-focusing nonlinearity. For this model, the linearized operator around a small solitary wave has an internal mode whose contribution to the dynamics is handled by checking a nonlinear condition related to the Fermi golden rule. Reference: Yvan Martel, Asymptotic stability of small standing solitary waves of the one-dimensional cubic-quintic Schrödinger equation, arXiv:2312.11016
12:00 - 13:30 (1h30)
Déjeuner
13:30 - 14:00 (30min)
Départ bus à 13h30
Départ bus à 13h30
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