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Lundi 10 Octobre
| Heure: |
14:00 - 17:00 |
| Lieu: |
IHP |
| Résumé: |
EDP & Physique mathématique - Séminaire Tournant IHP - |
Mardi 11 Octobre
| Heure: |
13:30 - 14:30 |
| Lieu: |
Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13 |
| Résumé: |
PM - EDP - Statistical mechanics of wave maps in dimension 1+1 - |
| Description: |
Jacek JendrejI will present a recent joint work with Brzezniak.We study wave maps with values in S^d, defined on the future light cone {|x|
<= t}, with prescribed data at the boundary {|x| = t}. Based on the work of
Keel and Tao, we prove that the problem is well-posed for locally absolutely
continuous boundary data. We design a discrete version of the problem and prove
that for every absolutely continuous boundary data, the sequence of solutions
of the discretised problem converges to the corresponding continuous wave map
as the mesh size tends to 0. Next, we consider the boundary data given by the
S^d-valued Brownian motion. We prove that the sequence of solutions of the
discretised problems has an accumulation point for the topology of locally
uniform convergence. We argue that the resulting random field can be
interpreted as the wave-map evolution corresponding to the initial data given
by the Gibbs distribution. |
Mercredi 12 Octobre
| Heure: |
13:30 - 15:00 |
| Lieu: |
Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13 |
| Résumé: |
Théorie Ergodique et Systèmes Dynamiques - Séminaire reporté (Propreté forte et stabilité des quotients compacts d’espaces homogènes réductifs) - |
| Description: |
Nicolas Tholozan, séance reportée
Soit G/H un espace homogène où G et H sont des groupes de Lie réels réductifs, et Gamma un sous-groupe discret de G agissant proprement discontinument et cocompactement sur G/H. Lorsque le groupe Gamma n’est pas rigide dans G, il est naturel de se demander si ses déformations continuent à agir proprement discontinument. Dans un travail en commun avec Fanny Kassel, nous  répondons affirmativement à cette question dans le cas où les rangs réels de G et H diffèrent de 1. Pour cela, nous montrons que les groupes agissant proprement discontinument et cocompactement sur un espace homogène réductif vérifie une propriété de propreté forte qui, en co-rang 1, s’apparente à une propriété d’Anosov (au sens de Labourie). |
Jeudi 13 Octobre
| Heure: |
10:15 - 12:00 |
| Lieu: |
Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13 |
| Résumé: |
Topologie algébrique - Derived Clifford algebra - |
| Description: |
Xuan Bach Nguyen
The Clifford algebra of a quadratic form is a very
classical object which plays an important part in the theory of
quadratic form. Several generalizations of the Clifford algebra
have been studied, for example, by replacing quadratic forms by
polynomial forms of higher degree. The study of these algebras
suggest that they can be defined geometrically. In this talk, we
will give the adjunction that realizes these generalizations and
we will introduce the derived Clifford algebra. |
Vendredi 14 Octobre
| Heure: |
10:30 - 12:00 |
| Lieu: |
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13 |
| Résumé: |
Géométrie Arithmétique et Motivique - Supersingular main conjectures, Sylvester's conjecture and Goldfeld's conjecture - |
| Description: |
Daniel KrizI will present a rank 0 and 1 p-converse theorem for CM elliptic
curves defined over the rationals in the case where p is ramified in the
CM field. This theorem has applications to two classical problems of
arithmetic: it verifies Sylvester's conjecture on primes expressible as a
sum of two rational cubes and establishes Goldfeld's conjecture for the
congruent number family. The proof relies on formulating and proving a
new Iwasawa main conjecture, which in turn involves new methods arising
from interplays between Iwasawa-theoretic objects and relative p-adic
Hodge theory on the infinite-level Shimura curve. |
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