5 mai 2021

Xu Yuan (Ecole Polytechnique)
Construction of multi-solitons for the energy-critical wave equation

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Lieu : https://bbb.imo.universite-paris-saclay.fr/b/nic-jog-f24-z6j

Résumé : We will review some results on the construction and interaction of solitary waves for the energy-critical focusing wave equation. After discussing briefly the well-known conjecture of soliton resolution, we will present recent results of the existence of multi-solitary waves in the case of weak interactions.

Construction of multi-solitons for the energy-critical wave equation  Version PDF

Céline Bonandrini (LMO)
Slope stability on Riemann surfaces

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Lieu : Salle 3L8 (a priori en distanciel pour l'instant)

Résumé : (english traduction below)
En géométrie algébrique, les conditions de stabilité permettent de construire de « bons » espaces de modules. Même si la définition générale est assez technique, dans le cas des surfaces de Riemann, la « slope stability » peut-être exprimée en termes de théorie des représentations, ou de géométrie différentielle.
Dans cet exposé je vais commencer par définir la condition de stabilité « slope stability » pour les surfaces de Riemann, puis donner une idée de la preuve du théorème de Narasimhan et Seshadri. Ce théorème donne une correspondance entre certains fibrés vectoriels stables et certaines représentations irréductibles et unitaires. Il existe aussi une correspondance entre les fibrés vectoriels stables et les fibrés Einstein-hermitiens, que j’évoquerai si le temps le permet.



In algebraic geometry, stability conditions are useful to produce nice moduli spaces. Although the general definition is quite technical, in the case of Riemann surfaces, slope stability can be rephrased in terms of representation theory, or differential geometry.
In this talk I will define slope stability on Riemann surfaces, and sketch an idea of the proof of Narasimhan and Seshadri’s theorem. This theorem gives a correspondence between some stable vector bundles and some irreducible unitary representations. There is also a correspondence between stable vector bundles and Einstein-Hermitian vector bundles, which I may mention if time allows it.

Slope stability on Riemann surfaces  Version PDF

Duong Phong (Columbia)
Geometric Partial Differential Equations from Unified String Theories

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Lieu : Demander le lien Zoom à jean-michel.bismut@universite-paris-saclay.fr

Résumé : The laws of nature at its fundamental level have long been a source of inspiration for geometry and partial differential equations. With unified string theories and particularly supersymmetry, a particularly important new requirement has emerged, which is that of special holonomy. The earliest manifestation was identified by Candelas, Horowitz, Strominger, and Witten in 1985 as the Calabi-Yau condition, but more general spaces have emerged since, that can be interpreted as generalizations of the Calabi-Yau condition to both non-Kaehler complex geometry and symplectic geometry. The corresponding equations are interesting in their own right from the point of view of the theory of non-linear partial differential equations. We shall survey some of these developments, with emphasis on the analytic open problems.

Geometric Partial Differential Equations from Unified String Theories  Version PDF