actualités

Cette thèse est consacrée à l'étude spectrale de l'opérateur de Schrödinger avec un champ purement magnétique et variable dans la limite semi-classique. Dans la première partie, nous travaillons en dimension 2 avec annulation du champ magnétique sur une courbe fermée. Sous des hypothèses génériques et symétriques, nous établissons une estimation, exponentiellement petite en terme d'un paramètre semi-classique noté par h, de la différence entre les deux premières valeurs propres du Laplacien magnétique, caractéristique de l'effet tunnel le long de la courbe d'annulation. Dans la deuxième partie, nous travaillons  en dimension 3 avec un champ magnétique variable dans un domaine ouvert, borné et régulier avec la condition de Neumann aux bord. Avec des hypothèses génériques, nous obtenons une asymptotique complète pour les petites valeurs propres du Laplacien magnétique.

Lieu : Nantes Université, faculté des sciences et techniques, bâtiment 2, amphithéâtre Pasteur.

Cette semaine marque le retour des 5 minutes Lebesgue. Nous aurons le plaisir d'écouter Erwan Brugallé dans un exposé intitulé :

Voici le résumé:

"J'essaierai de vous convaincre en 5 minutes qu'il n'est pas totalement farfelu d'appeler "droite" un tripode dans le plan."

La séance sera suivi du visionnage de quelques exposés rennais.

Lieu : Nantes Université, UFR Sciences et techniques , bâtiment 10, salle 3.

Pièce biographique, en anglais, sur Emmy Noether, mathématicienne remarquable du 20e siècle.

En savoir +

Inscription nominative, gratuite mais obligatoire : https://www.eventbrite.fr/e/billets-diving-into-math-with-emmy-noether-741475361767?aff=oddtdtcreator

amphi Pasteur

Titre de la thèse : Test à noyaux et leurs applications aux données single-cell.

Résumé : Les technologies de single-cell génèrent des données qui présentent de nombreux défis, il y a beaucoup d'observations, elles sont en grande dimension et souvent parcimonieuses. De nombreuses expériences de biologie consistent à comparer des conditions. L'objet de la thèse est de développer un ensemble d'outils qui permet de comparer des échantillons de données issues des technologies single-cell afin de détecter et éventuellement décrire les différences qui existent. Pour cela, j'applique les tests de comparaison de deux échantillons basés sur les méthodes à noyaux existants et propose un nouveau test qui généralise ces méthodes pour un design expérimental quelconque. Je discuterai aussi l'implémentation et l'utilisation des tests. Afin que ces outils soient accessibles et utilisables par des non-spécialistes, je propose un ensemble de méthodes pour le diagnostic et l'interprétation des résultats.

Centrale Nantes : Amphi du Batiment S

10h30-11h30 - Andras Stipsicz (Reny Institut Budapest)
"Z_2-actions on four-manifolds"

Abstract:
Exotic smooth structures on four-manifolds are one of the most surprising, and at the same time most fascinating phenomena in low dimensional topology. Existence questions of exotic smooth structures on closed simply connected four-manifolds with definite intersection form are of central importance — as a special case, this problem includes the smooth four-dimensional Poincaré conjecture.
We show exotic examples of definite four-manifolds with fundamental group Z_2.
In another direction, Z_2-actions on specific exotic four-manifolds provide embeddings of connected sums of the real projective plane RP^{^2} to the four-sphere S^{^4} which are topologically standard, but smoothly not.
Smooth exotica are proved using Seiberg-Witten theory — we will hint the use of these invariants in this context.

14h00-15h00 - Vincent Florens (Université de Pau)
"Topological invariants of line arrangements"

Abstract:
A line arrangement is a finite set of lines in the complex projectiveplane CP2. They are  particular cases of plane algebraic curves where the components have all degree 1. We are interested in the influence of the combinatorial data of an arrangement on its embedded topology in CP2.
The boundary manifold of an arrangement is the common boundary of a regular neighborhood of the arrangement and its exterior. This is a graph three-manifold, in the sense of Waldhausen, whose topology is completly determined by the combinatorics. We use the inclusion map of the boundary manifold in the exterior to construct a new topological invariant of arrangements. This is a joint work with E.Artal and A.Rodau.

15h30-16h30 - Discussions

10h30-11h30 - Andras Stipsicz (Reny Institut Budapest)
"Z_2-actions on four-manifolds"

Abstract:
Exotic smooth structures on four-manifolds are one of the most surprising, and at the same time most fascinating phenomena in low dimensional topology. Existence questions of exotic smooth structures on closed simply connected four-manifolds with definite intersection form are of central importance — as a special case, this problem includes the smooth four-dimensional Poincaré conjecture.
We show exotic examples of definite four-manifolds with fundamental group Z_2.
In another direction, Z_2-actions on specific exotic four-manifolds provide embeddings of connected sums of the real projective plane RP^{^2} to the four-sphere S^{^4} which are topologically standard, but smoothly not.
Smooth exotica are proved using Seiberg-Witten theory — we will hint the use of these invariants in this context.

14h00-15h00 - Vincent Florens (Université de Pau)
"Topological invariants of line arrangements"

Abstract:
A line arrangement is a finite set of lines in the complex projectiveplane CP2. They are  particular cases of plane algebraic curves where the components have all degree 1. We are interested in the influence of the combinatorial data of an arrangement on its embedded topology in CP2.
The boundary manifold of an arrangement is the common boundary of a regular neighborhood of the arrangement and its exterior. This is a graph three-manifold, in the sense of Waldhausen, whose topology is completly determined by the combinatorics. We use the inclusion map of the boundary manifold in the exterior to construct a new topological invariant of arrangements. This is a joint work with E.Artal and A.Rodau.

15h30-16h30 - Discussions

La troisième séance de conférences Master sera l'occasion d'écouter Imène Bouafia (M2 IS) et Marie Compain (M2 MACS) qui nous parleront de leur expérience de stage de M1.

Plus précisément,
- Imène Bouafia parlera de Statistiques Bayésiennes et contraintes Stratigraphiques (Stage réalisé au LMJL),
- Marie Compain parlera de Simulations numériques d’une solution de référence pour les phénomènes viscothermiques dans les instruments de musique à vent (Stage réalisé à Inria Bordeaux).

Ce sera en amphi D.

La deuxième séance de conférences Master sera l'occasion d'écouter Florian Loiseau (M2 MFA), Manon Simonot (M2 IS) et Matthieu Trotreau (M2 IS) qui nous parleront de leur expérience de stage de M1.

Plus précisément,
- Florian Loiseau parlera de sa "Formation en théorie des nombres" (stage réalisé à l'Université de Lille),
- Manon Simonot présentera la "Conception d'une application web comme outil clinique d'aide à l'analyse et au suivi des troubles de la marche" (stage réalisé au LMJL UMR 6629 Nantes Université),
- Matthieu Trotreau exposera sur "Les déterminants d’une carrière hospitalo-universitaire, sous la perspective du genre" (stage réalisé au Laboratoire de Psychologie de Nantes Université (LPPL - UR 4638)).

Amphi D
 

Rencontre ANR - salle Eole

Wednesday 27 :
2pm -> 3pm :           Frédéric Rousset (Université Paris-Saclay), Interaction of a solitary water wave with a slowly varying bottom
3.30pm -> 4.30pm : Beatrice Langella (SISSA), Time periodic solutions of resonant Klein-Gordon equations on the 3d sphere

Thursday 28 :
9:30am->10:30am : Francisco Torres de Lizaur (University of Seville), Quasiperiodic solutions and invariant manifolds in the Euler equation of hydrodynamics
11am -> 12am :       Fernando Casas (Universitat Jaume I), A short introduction to splitting methods for differential equations

2pm->3pm :             Yoann Le Hénaff (Université Rennes 1), Grid-free Weighted Particle method applied to the Vlasov-Poisson equation
3:30pm->4:30pm :   Qi Zhou (NanKai University), Quantitative structured almost reducibility and its applications

Friday 29:
9:30am->10:30am : Michela Procesi (Università Roma Tre), Almost-periodic solutions for the NLS with convolution potential

11am -> 12am :       Zhiyan Zhao (Université Côte d’Azur), Symplectic Normal Forms and Classification of Growth of Sobolev norms

Et les résumés  :

Frédéric Rousset : Interaction of a solitary water wave with a slowly varying bottom

In this talk we will discuss how a solution of the water wave system which behaves like a pure solitary wave at infinity  is influenced by a slowly varying monotonously increasing or decreasing bottom. The main framework will be the water wave system with strong  surface tension but we shall also use a Whitham type equation to illustrate the ideas. Joint work with Maria Eugenia Martinez (Lyon) and Claudio Munoz (Santiago).

Beatrice Langella : Time periodic solutions of resonant Klein-Gordon equations on the 3d sphere

In this talk I will focus on a class of completely resonant Klein-Gordon equations on the 3 dimensional sphere $\mathbb{S}^3$ with quadratic, cubic and quintic nonlinearity, which arise as toy models in General Relativity. I will show that these equations admit small amplitude, time periodic solutions. Their existence is obtained by a variational Lyapunov-Schmidt decomposition, which reduces the problem to the search of Mountain Pass critical points of a restricted Euler-Lagrange action functional.
In order to gain compactness of the gradient of such a functional and smoothness of the critical points, a key point is to implement Strichartz-type estimates for the solutions of the linear Klein-Gordon equation on $\mathbb{S}^3$. Based on a joint work with Massimiliano Berti and Diego Silimbani.

Francisco Torres de Lizaur : Quasiperiodic solutions and invariant manifolds in the Euler equation of hydrodynamics

I will review recent results on existence and dynamics of finite dimensional invariant manifolds of the Euler equation. These are families of divergence-free vector fields, parametrized by some manifold N, with the property that the solutions of the Euler equation with initial condition in the family exist and remain there for all time, defining a finite-dimensional ODE on N. For example if N is a torus and the ODE is a linear flow, these give families of periodic or quasiperiodic solutions of the Euler equation. This is joint work with A. Enciso and D. Peralta-Salas.

Fernando Casas : A short introduction to splitting methods for differential equations

Splitting methods constitute a powerful tool for the numerical integration of differential equations, either arising directly from dynamical systems or from partial differential equations of evolution previously discretized in space. Efficient high-order schemes have been designed that provide accurate solutions whilst preserving some of the most salient qualitative features of the system. In this talk we present an overview of this type of schemes and some of their applications. We will also consider a new class of reversible splitting methods and analyze their preservation properties when they are applied to the integration of unitary problems.

Yoann Le Hénaff : Grid-free Weighted Particle method applied to the Vlasov-Poisson equation

In this talk, a particle method for the collisionless Vlasov-Poisson system will be presented. It is based on the exact representation of an approximate electric field and, thanks to its grid-free nature, circumvents some of the usual drawbacks of PIC-like methods. Convergence and numerical aspects will be presented.

Qi Zhou : Quantitative structured almost reducibility and its applications

We propose a method called quantitative structured almost reducibility for analytic quasiperiodic $SL(2,\R)$-cocycles, which allows us to deal with infinitely many normal frequency resonances. Also we give will its dynamical and spectral applications.

Michela Procesi : Almost-periodic solutions for the NLS with convolution potential

I shall discuss some recent results, in collaboration with Livia Corsi and Guido Gentile proving the existence of maximal invariant tori for the NLS with a convolution potential of arbitrary regularity.

Zhiyan Zhao : Symplectic Normal Forms and Classification of Growth of Sobolev norms

For the Hamiltonian PDEs quantized by a quadratic polynomial with time-dependent coefficients, we give a complete classification for the long-time behaviors of the solution in Sobolev space, through Metaplectic representation and Schrödinger representation. Every behavior of Sobolev norm is characterized by a certain symplectic normal form by means of reducibility.
 

I will discuss some results about surfaces in with conical singularities 4-manifolds ("PL surfaces") and about symplectic curves in symplectic 4-manifolds.
Je discuterai quelques résultats autours des surfaces à singularités coniques dans le 4-variétés (« surfaces PL ») et des courbes symplectiques dans le 4-variétés symplectiques.

Rapporteurs : Julien Marché (Sorbonne Université), András Stipsicz (Rényi Institute of Mathematics), Daniel Ruberman (Brandeis University)

Campus Lombarderie, Bâtiment 11, salle 3. Un lien zoom sera disponible sur demande.