Les événements de avril 2018

• Jeudi 26 avril 11:00-12:00 - Roberta Tittarelli

Séminaire d’Analyse Numérique et Calcul Scientifique

• Vendredi 27 avril 13:30-14:30 - Edoardo Bocchi - Institut de Mathématiques de Bordeaux

Séminaire doctorant : Floating structures in shallow water : local well-posedness in the axisymmetric case.

Résumé :
The floating structure problem describes the interaction between surface water waves and a floating body, generally a boat or a wave energy converter. As shown by Lannes the equations for the fluid motion can be reduced to a set of two evolution equations on the surface elevation and the horizontal discharge. The presence of the object is accounted for by a constraint on the discharge under the object ; the pressure exerted by the fluid on this object is then the Lagrange multiplier associated with this constraint. Our goal is to prove the well-posedness of this fluid-structure interaction problem in the shallow water approximation under the assumption that the flow is axisymmetric without swirl. We write the fluid equations as a quasilinear hyperbolic mixed initial boundary value problem and the solid equation as a second order ODE coupled to the fluid equations. Finally we prove the local in time well-posedness for this coupled problem, provided some compatibility conditions on the initial data are satisfied.
References :
[1] E. BOCCHI, Floating structures in shallow water : local well-posedness in the axisymmetric case, arXiv preprint (2018)

Lieu : 324-2B

• Jeudi 5 avril 14:00-15:30 - Jishnu Ray - Laboratoire de Mathématiques d'Orsay

Sém. ATDN - Iwasawa algebras of $p$-adic Lie groups and Galois representations with open image

Résumé : A key tool in the study of algebraic number fields are Iwasawa algebras, originally constructed by Iwasawa in the 1960’s to study the "class groups" of fields, but since appearing in varied settings such as a Lazard’s work on p-adic Lie groups and Fontaine’s work on local Galois representations. For a prime p, the Iwasawa algebra of a p-adic Lie group G, denoted by Zp[ [G] ], is a non-commutative completed group algebra of G.
In the first part of the talk, we lay the foundation by giving a very explicit description of certain Iwasawa algebras (one such algebra was described by my advisor Clozel). The base change map between the Iwasawa algebras over extensions of Qp motivates us to discuss globally analytic p-adic representations following Emerton’s work.
In the second part of the talk, we will discuss about numerical experiments using a computer algebra system which give heuristic support to Greenberg’s p-rationality conjecture which affirms the existence of “p-rational” number fields with Galois groups (Z/2Z)^t\$. The p-rational fields are algebraic number fields whose Galois cohomology is particularly simple and which are interesting because they offer ways of constructing Galois representations with big open images. We go beyond Greenberg’s work and construct novel Galois representations of the absolute Galois group of Q with big open images in reductive groups over Zp (ex. GL(n ;Zp) ; SL(n ;Zp) ; SO(n ;Zp) ; Sp(n ;Zp)). We are proving results which show the existence of p-adic Lie extensions of Q where the Galois group corresponds to a certain specific p-adic Lie algebra (ex. sl(n) ; so(n) ; sp(2n)). This relates our work with a more general and classical Inverse Galois problem for p-adic Lie extensions.

Lieu : 324-2B

• Jeudi 26 avril 14:00-15:00 - Xavier Roblot - Institut Camille Jordan (Lyon)

Sém. ATDN - Sur la conjecture galoisienne de Brumer-Stark pour les groupes nilpotents

Résumé : Soit K/k une extension galoisienne de corps de nombres, la conjecture galoisienne de Brumer-Stark prédit essentiellement que l’élément de Brumer-Stickelberger, élément de l’anneau de groupe construit à partir des valeurs en 0 des fonctions L d’Artin associées à l’extension, annule le groupe de classes de K. Elle généralise au cas non abélien la conjecture (abélienne) de Brumer-Stark énoncée par Tate aux débuts des années 80. Dans cet exposé, j’expliquerai comment on peut déduire la conjecture galoisienne de la conjecture abélienne dans le cas des groupes nilpotents. La preuve passe par une étude de la décomposition des caractères induits de certains sous-groupes et notamment des treillis modulaires qu’on en déduit.

Lieu : 324-2B

• Mardi 3 avril 13:45-15:00 - Rauan Akylzhanov - Imperial College London

Smooth dense subalgebras and Fourier multipliers on compact quantum groups

Résumé : We define and study dense Frechet subalgebras of compact quantum groups consisting of elements rapidly decreasing with respect to an unbounded self-adjoint Dirac-like operator with compact resolvent. Further, we characterise the boundedness of its commutators in terms of the eigenvalues. Grotendieck’s theory of topological tensor products immediately yields a Schwartz kernel theorem for linear operators on compact quantum groups and allows us to introduce a natural class of pseudo-differential operators on compact quantum groups. Further, we show that composition of two regular pseudo-differential operators is a regular pseudo-differential operator. As a by-product, we develop elements of the distribution theory and corresponding Fourier analysis. We give applications of our construction to obtain sufficient conditions for Lp - Lq boundedness of coinvariant linear operators. We provide necessary and sufficient conditions for algebraic differential calculi on Hopf subalgebras of compact quantum groups to extend to the proposed smooth structure. We check explicitly that these conditions hold true on the quantum SUq(2) for both its 3-dimensional and 4-dimensional calculi.
Joint work with Michael Ruzhansky and Shahn Majid.

• Mardi 24 avril 13:45-15:00 - Yi-Jun YAO - Universite de Fudan

A propos d’un lemme de Connes

Résumé : Nous allons présenter les détails concernant Lemme VI.3.9 du livre "Noncommutative Geometry" d’Alain Connes.

• Vendredi 27 avril 15:00-16:30 - Uwe Franz - LMB

Groupe de Travail Information Quantique

Résumé : once more LOCC and Nielson’s majorisation theorem

Lieu : 324B-2, LMB - Batiment Métrologie, Campus Bouloie, Besançon

• Vendredi 6 avril -

Cinquième Journée des Jeunes Chercheurs en Mathématiques de l’UBFC

Lieu : Amphi A (UFR ST, Besançon)

• Lundi 16 avril 10:30-12:30 -

Soutenance de thèse de Marine ROUGNANT

Lieu : Amphi B (UFR ST, Besançon)