Nom de l'orateur
Seán Gomes
Etablissement de l'orateur
University of Helsinki
Lieu de l'exposé
salle des séminaires
Date et heure de l'exposé
Dans cet exposé, nous discutons d'une approche microlocale de Fredholm de la diffusion pour l'équation de Schrödinger non linéaire avec un potentiel supporté de manière compacte et une perturbation métrique euclidienne supportée de manière compacte. Nous montrons que l'opérateur de Schrödinger $P=D_t+\Delta_g+V$ est un opérateur de Fredholm (en fait inversible) entre des espaces de Sobolev convenablement définis et pondérés microlocalement et nous exploitons les propriétés de mappage résultantes pour résoudre NLS avec de petites données d'entrée asymptotiques prescrites (le soi-disant ''problème de l'état final''). Cette exposé est basée sur un travail conjoint avec Jesse Gell-Redman et Andrew Hassell.
Nom de l'orateur
Hedong Hou
Etablissement de l'orateur
Université Paris Saclay
Lieu de l'exposé
salle des séminaires
Date et heure de l'exposé

Used by the work of Koch-Tataru on Navier-Stokes equations, the theory of tent spaces turns out to be useful to deal with evolution equations with very rough initial data. In this talk, we shall discuss the recent progress on studying linear parabolic equations with time-independent, uniformly elliptic, bounded measurable complex coefficients via tent spaces. The talk is based on a joint work with Pascal Auscher.

Nom de l'orateur
Paolo Aceto
Etablissement de l'orateur
Université de Lille
Lieu de l'exposé
Salle des séminaires
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Motivated by the study of smoothings of rational surface singularities as well as symplectic f illings of plumbed 3-manifolds, we consider an analogue problem in a purely topological setting. The question of when a rational surface singularity admits a unique smoothing is of particular interest and has led to a conjecture of Kollár which has been proved in some cases. We look at smooth, definite fillings of certain plumbed manifolds and consider the question of which intersection forms can be realized by such fillings. We describe various constructions and an obstruction based on Donaldson’s diagonalization theorem.

Nom de l'orateur
Russell Avdek
Etablissement de l'orateur
Laboratoire de Mathématiques d'Orsay
Lieu de l'exposé
Salle des séminaires
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We'll define stabilization for codim=2 contact manifolds of dim>3 contact manifolds so that the following holds: A contact manifold is overtwisted iff its "standard contact unknot" is a stabilization. This means that many dim=2n+1>3 contact manifolds contain dim=2n-1 spheres which are unknotted smoothly but "knotted" from a contact-topological point of view.

Nom de l'orateur
Johannes Rau
Etablissement de l'orateur
Université de Los Andes
Lieu de l'exposé
Salle Eole
Date et heure de l'exposé

(Joint with Erwan Brugallé and Lucía López de Medrano.) Combinatorial patchworking is a technique introduced by Viro to study the topology of real algebraic hypersurfaces. It's base ingredients are a triangulation of a lattice polytope and a sign distribution on its vertices. If the triangulation is "convex", the construction can be translated to the dual setting of tropical varieties. In recent years, this dual viewpoint has promoted new results using tropical homology theories. For example, Renaudineau and Shaw proved a conjecture by Itenberg bounding the Betti numbers of the real part of a (unimodular) patchwork hypersurface in terms of the Hodge numbers of the complex part.

Nom de l'orateur
Lisa Lokteva
Etablissement de l'orateur
Glasgow University
Lieu de l'exposé
Salle des séminaires
Date et heure de l'exposé

The subject jokingly called "3.5-dimensional topology" concerns itself with the interactions between 3-manifolds and 4-manifolds, asking, given a 3-manifold, what 4-manifolds it is the boundary of. One big question in 3.5-dimensional topology is when a rational homology 3-sphere is the boundary of a rational homology 4-ball. (Guess what? Almost never.) We will discuss this question for a particular class of rational homology 3-spheres described by weighted graphs, presenting some results, conjectures, and ways forward.

Nom de l'orateur
NGUYEN THAC DUNG
Etablissement de l'orateur
VNU-University of Science, Hanoi
Lieu de l'exposé
Salle des séminaires
Date et heure de l'exposé

In this talk, we will review the recent works by Petersen and Wink regarding new curvature conditions for Bochner techniques on closed manifolds and its applications. Then, we continue there techniques to study non-compact complete manifolds and show several rigidity results of harmonic tensors in terms of Lichnerowicz Laplacians. Several applications to study geometry of curved manifolds and immersed submanifolds are also given .

Nom de l'orateur
Carlos Villegas Blas
Etablissement de l'orateur
Universidad Nacional Autónoma de México
Lieu de l'exposé
salle des séminaires
Date et heure de l'exposé
In this talk we consider the Dirichlet to Neumann map (D-N) for the unit sphere in $R^3$. When we are sufficiently far from the origin, the spectrum of such an operator consists of eigenvalue clusters around the natural numbers. The distribution of the corresponding scaled eigenvalue shifts has an asymptotic expansion when the label of the cluster goes to infinity. The asymptotic expansion consists of distributions called spectral invariants.