événements à venir
Dans ce séminaire, je vais m'intéresser aux solutions positives de l'équation suivante:
où est une fonction de classe et est un domaine non borné et où l'on a imposé des conditions de Dirichlet homogène sur le bord. L'idée est de classer de telles solutions en fonction de leurs propriétés géométriques (unidimensionnelles, nulles, ...). L'exposé sera divisé en deux parties, une première partie introductive où je présenterai les résultats existants dans ce cadre, et une seconde partie où j'énoncerai de nouveaux résultats que l'on a mis en évidence en collaboration avec A. Farina et B. Sciunzi.
TBA
This talk will mainly focus on recent work on the SPR property for surface diffeomorphisms, as well as our latest results.
The SPR property is a classical notion in symbolic dynamics and implies important statistical properties such as exponential mixing. Recently, Buzzi-Crovisier-Sarig introduced the notion of SPR for surface diffeomorphisms, provided equivalent characterizations of this property, and established exponential mixing for measures of maximal entropy.
We establish the SPR property for equilibrium states of a class of potentials, weaken the conditions required for SPR, and provide an effective form of the SPR property for surface diffeomorphisms.
TBA
The symmetric group appears in the Schur–Weyl duality describing the centralisers of tensor powers of the vector representation of the linear group. We would like to generalize this result to a new algebra called the fused permutations algebra. This last one was introduced recently for this purpose.
The first main goal will be to give an algebraic presentation of the fused permutations algebra, for a particular case, and a canonical basis. In particular, we prove that the fused permutations algebra is a quotient of the degenerate cyclotomic affine Hecke algebra, and we also describe a basis of this latter algebra combinatorially in terms of signed permutations with avoiding patterns.
The second main purpose, which comes from the first one, is the study of primitive idempotents of the cylotomic degenerate affine Hecke algebra. More precisely, we give a decomposition of these in a certain basis indexed by the elements of the Coxeter group of type B.
TBA