Statut  Confirmé 
Série  SEMINFOR 
Domaines  condmat.statmech 
Date  Jeudi 14 Septembre 2017 
Heure  11:00 
Institut  LPTHE 
Salle  Bibliothèque 
Nom de l'orateur  BlondeauFournier 
Prenom de l'orateur  Olivier 
Addresse email de l'orateur  
Institution de l'orateur  Université Laval, Québec 
Titre  The KP hierarchy and its superspace construction 
Résumé  The KadomtsevPetviashvili (KP) hierarchy is a dynamical system that can be viewed as defined on a infinite dimensional Grassmannian and which contains an infinite tower of nonlinear differential equations. This system is completely integrable, meaning that one can find all the conserved quantities, and the various solutions are known exactly. The KP hierarchy interplays with many physical system, such as the related KdV system, and is equivalently formulated as a bosonfermion correspondence. This latter construction is of particular interest since it beautifully connects with the theory of symmetric polynomials, through the formalism of vertex operators and Bernstein operators. In view of its great impact in mathematical physics, the KP hierarchy can be extended to include larger classes of systems with the supersymmetry. In this talk, I will first show a brief review of the KP hierarchy system focusing on its connection with symmetric polynomials and in particular the Schur functions. Then, I will present my recent work on the supersymmetric generalization of the KP hierarchy from the point of view of a superspace analogue of the Bernstein operators. 
Numéro de preprint arXiv  
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