{"id":181,"date":"2015-02-01T15:59:56","date_gmt":"2015-02-01T13:59:56","guid":{"rendered":"http:\/\/sites.univ-tln.fr\/master-math\/?p=181"},"modified":"2016-10-21T16:07:30","modified_gmt":"2016-10-21T14:07:30","slug":"topics-2014-2015","status":"publish","type":"post","link":"https:\/\/sites.univ-tln.fr\/master-math\/en\/topics-2014-2015\/","title":{"rendered":"Topics 2014-2015"},"content":{"rendered":"
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  1. [M2] J.-J. Alibert (IMATH)<\/b> In\u00e9galit\u00e9s de Sobolev-Poincar\u00e9.<\/i>
    \nCes in\u00e9galit\u00e9s peuvent \u00eatre utilis\u00e9es pour valider certains r\u00e9sultats de Gamma-convergence de fonctionnelles sur l’espace des mesures bor\u00e9liennes born\u00e9es du plan. Ces r\u00e9sultats de Gamma-convergence valident certains mod\u00e8les continus en m\u00e9canique du solide par exemple.<\/li>\n
  2. [M1\/2] J. Asch<\/a> (CPT) <\/b> Occurrence of conical eigenvalue crossings.<\/i>
    \nThe object is to study the occurrence of conical eigenvalue intersections in a basic model of solid state quantum theory. In reference [1] these are shown to occur for the family of operators (-id_x-k)^2+V(x) on L^2(T) where T is a torus, V belongs to a certain class of functions, k varies in the dual torus which is related to a honeycomb lattice. The work to be done is to study reference [1] and to exhibit a way to prove stability of the result under deformations of the honeycomb structure.
    \nPrerequisites: Basic Functional Analysis, Operator and Spectral Perturbation theory.
    \nReferences:
    \n[1] C.L. Fefferman, M.L. Weinstein, Honeycomb lattice potentials and Dirac points, Journal of the American Mathematical Society, 25 (4), 2012, 1160-1220<\/li>\n
  3. [M2] W. Aschbacher<\/a> (CPT) <\/b> The fermionic Federbush model.<\/i>
    \nAlthough the standard model of particle physics is the fundamental conceptual framework for the description of the elementary particles and the strong and electroweak forces between them, it does not yet have the status of a physical theory in the sense that a rigorous mathematical construction and a proof of its consistency are still lacking (see the millenium problem \u00ab\u00a0Yang-Mills and mass gap\u00a0\u00bb). Important contributions to this question were made in the program of constructive quantum field theory initiated by Glimm and Jaffe in the middle of the 60ies. Unfortunately, this program could not reach its goal of constructing an interacting theory in the physically relevant four spacetime dimensions, but, based on Wightman’s axioms, existence and consistency of interacting quantum field theoretical models in two and three spacetime dimensions have been rigorously established. I propose to study the so-called fermionic Federbush model which describes two species of interacting fermions in two spacetime dimensions. The Federbush model was the first relativistic field theory model for which not only the Wightman axioms but also asymptotic completeness have been rigorously proved.
    \nReferences:
    \n[1] Ruijsenaars S N M, The Wightman axioms for the fermionic Federbush model<\/i>, Commun. Math. Phys. 87 (1982) 181-228
    \n[2] Ruijsenaars S N M, Integrable quantum field theories and Bogoliubov transformations<\/i>, Ann. Phys. 132 (1981) 328-382
    \n[3] Summers S J, A perspective on constructive quantum field theory<\/i>, http:\/\/arxiv.org\/abs\/1203.3991 (2012)<\/li>\n
  4. [M2] Y. Aubry<\/a> (IMATH) <\/b> Du th\u00e9or\u00e8me de l’indice de Hodge aux nombres de points des courbes sur les corps finis.<\/i>
    \nCf.     ici <\/a><\/li>\n
  5. [M2] Y. Aubry<\/a> (IMATH) <\/b> Corps de fonctions de nombre de classes 1.<\/i>
    \nIl s’agit d’\u00e9tudier l’article Function fields of class number one<\/i> de Qibin Shen, Shuhui Shi publi\u00e9 sur arXiv le 6 f\u00e9vrier 2015.
    \nAbstract:
    \nIn 1975, [LMQ] listed 7 function fields over finite felds (up to isomorphism) with positive genus and class number (i.e., the size of the divisor class group of degree zero) one and claimed to prove that these were the only ones such. In [S1], Claude Strirpe found 8th one! In this paper, we fix the argument in [LMQ] to show that this 8th example could have been found by [LMQ] method and is the only one, so that the list is now complete.
    \nReferences:
    \n[1] arXiv:1412.3505<\/li>\n
  6. [M1\/2] J.-M. Barbaroux<\/a> (CPT) <\/b> R\u00e9gularit\u00e9 des solutions de l’\u00e9quation de Boltzmann homog\u00e8ne.<\/i>
    \nCf.     ici <\/a><\/li>\n
  7. [M1\/2] G. Bouchitt\u00e9<\/a> (IMATH) <\/b> Distances entre probabilit\u00e9s: quelques variantes de la distance de Wasserstein et applications en statistiques.<\/i><\/li>\n
  8. [M1\/2] F. Chittaro<\/a> (LSIS) <\/b> Control of bilinear Schr\u00f6dinger equations.<\/i>
    \nCf.     ici <\/a><\/li>\n
  9. [M1\/2] F. Chittaro<\/a> (LSIS) <\/b> How rare are multiple eigenvalues?<\/i>
    \nCf.     ici <\/a><\/li>\n
  10. [M1\/2] F. Chittaro<\/a> (LSIS) <\/b> G\u00e9om\u00e9trie sous-Riemannienne.<\/i>
    \nCf.     ici <\/a><\/li>\n
  11. [M1\/2] M. Ersoy<\/a> (IMATH) <\/b> <\/i>
    \nThe first topic is to construct a robust and accurate kinetic scheme. Up to now, there are no well-balanced and entropic numerical scheme constructed from the kinetic approach when the source term is complex. Thus, we mainly focus on how to construct such a scheme which are designeds to solve hyperbolic systems of equations, e.g. Saint-Venant.<\/li>\n
  12. [M1\/2] M. Ersoy<\/a> (IMATH) <\/b> <\/i>
    \nThis topic deals with the rigorous justification of the Saint-Venant-Exner equations for sediment transport for which it is well-known that Exner equation governs the morphodynamic part of the flow and Saint-Venant the hydrodynamic one. These equations are coupled through the topography term. The idea is to use the Vlasov equation for the sediment transport modeling and the Euler equation for the fluid. The main task will be to define correctly the modeling of the kinetic boundary conditions (which describes incoming and outgoing sediment particles). Hydrodynamic limit and a thin layer asymptotic analysis will be used to get a sediment transport model.<\/li>\n
  13. [M1\/2] M. Ersoy<\/a> (IMATH) <\/b> <\/i>
    \nThis topic concerns an exact Riemann solver for a general coupled hyperbolic systems trough a discontinuous flux gradient. This arise, for instance, in the modeling of unsteady mixed flows in closed water pipes for which the sound speed is necessary continuous with a discontinuous gradient leading to a discontinuous flux gradient. The main task is then to define rigorously the solution through the discontinuity which is not necessary fixed.<\/li>\n
  14. [M1\/2] C. Galusinski<\/a> (IMATH) <\/b> Condition limite en entr\u00e9e et sortie pour un \u00e9coulement incompressible \u00e0 Reynolds \u00e9lev\u00e9.<\/i>
    \nCf.     ici <\/a><\/li>\n
  15. [M1\/2] C. Galusinski<\/a> (IMATH) <\/b> Suivi d’interfaces par maillage cart\u00e9sien mouvant.<\/i>
    \nCf.     ici <\/a><\/li>\n
  16. [M1] H. Jaber (CPT) <\/b> Principe du maximum. <\/i>
    \nCf.     ici <\/a><\/li>\n
  17. [M1\/2] S. Meradji<\/a> (CPT\/IMATH) <\/b> Modeling of flame spread in engineered cardboard fuelbeds.<\/i>
    \nCf.     ici <\/a><\/li>\n
  18. [M1\/2] C. Pid\u00e9ri (IMATH) <\/b> Comportement effectif d’un mat\u00e9riau homog\u00e8ne avec inclusions \u00e9lastiques.<\/i>
    \nOn se propose d’\u00e9tudier le comportement d’un mat\u00e9riau \u00e9lastique \u03a9 qui contient des inclusions \u00e9lastiques r\u00e9parties p\u00e9riodiquement au voisinage d’un segment \u0393. En dehors de cette zone, le mat\u00e9riau est homog\u00e8ne. En premi\u00e8re approximation, les inclusions n’ont aucune influence sur le comportement global du mat\u00e9riau et nous cherchons \u00e0 comprendre leur effet au second ordre. Pour cela nous utiliserons une m\u00e9thode de double \u00e9chelle bas\u00e9e sur les d\u00e9veloppements asymptotiques raccord\u00e9s. Une fois cette \u00e9tape franchie, on pourrait s’int\u00e9resser au cas o\u00f9 les inclusions sont rigides.
    \nCf.     ici <\/a><\/li>\n
  19. [M1\/2] C.-A. Pillet<\/a> (CPT) <\/b> Riemannian geometry, statistical mechanics, and thermodynamics.<\/i>
    \nCf.     ici <\/a><\/li>\n
  20. [M1\/2] M. Rouleux (CPT) <\/b> Ionization properties of an atom in a periodic electric field: the semi-classical approach. <\/i>
    \nCf.     ici <\/a><\/li>\n
  21. [M2] P. Seppecher<\/a> (IMATH) <\/b> Effet du contraste sur la pertinence des mod\u00e8les homog\u00e9n\u00e9is\u00e9s en \u00e9lasticit\u00e9.<\/i>
    \nCf.     ici <\/a><\/li>\n
  22. [M1] S. Vaienti<\/a> (CPT) <\/b> Principe d’invariance et th\u00e8oreme de Donsker.<\/i>
    \nLe principe d’invariance est un raffinement du theor\u00e8me central limite. En introduisant de mani\u00e8re convenable un temps continu, on montre la convergence de la somme de variables al\u00e9atoires vers un mouvement brownien.<\/li>\n<\/ol>\n<\/div>\n

     <\/p>\n

    Other Research Institutes<\/strong><\/div>\n
    \n
      \n
    1. [M2] IMFT<\/a> <\/b> Impl\u00e9mentation et validation dans un code de DNS d’\u00e9coulements particulaires du d\u00e9placement et des collisions pour des particules solides et non-sph\u00e9riques.<\/i>
      \nCf.       ici <\/a><\/li>\n
    2. [M2] INRA<\/a> <\/b> Etude num\u00e9rique d’un mod\u00e8le de r\u00e9action-advection-diffusion \u00e0 advection h\u00e9t\u00e9rog\u00e8ne d\u00e9finie \u00e0 partir de noyaux de perception.<\/i>
      \nCf.       ici <\/a><\/li>\n<\/ol>\n<\/div>\n
      Companies<\/strong><\/div>\n
      \n
        \n
      1. [M2] Dassault Syst\u00e8mes <\/a> <\/b> Simulation comportementale massivement distribu\u00e9e.<\/i>
        \nCf.         ici <\/a><\/li>\n<\/ol>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

        [M2] J.-J. Alibert (IMATH) In\u00e9galit\u00e9s de Sobolev-Poincar\u00e9. Ces in\u00e9galit\u00e9s peuvent \u00eatre utilis\u00e9es pour valider certains r\u00e9sultats de Gamma-convergence de fonctionnelles sur l’espace des mesures bor\u00e9liennes born\u00e9es du plan. Ces r\u00e9sultats de Gamma-convergence valident certains mod\u00e8les continus en m\u00e9canique du solide par exemple. [M1\/2] J. Asch (CPT) Occurrence of conical eigenvalue crossings. The object is to […]<\/p>\n","protected":false},"author":11,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[19],"tags":[],"class_list":["post-181","post","type-post","status-publish","format-standard","hentry","category-master-thesis-topics"],"_links":{"self":[{"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/posts\/181","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/comments?post=181"}],"version-history":[{"count":2,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/posts\/181\/revisions"}],"predecessor-version":[{"id":190,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/posts\/181\/revisions\/190"}],"wp:attachment":[{"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/media?parent=181"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/categories?post=181"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.univ-tln.fr\/master-math\/wp-json\/wp\/v2\/tags?post=181"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}