Centre de Physique Théorique

Agenda

Jeudi 16 novembre 2017

XIIIe Ecole de Cosmologie

XIIIe Ecole de Cosmologie

Ecole thématique du CNRS organisée par François Bouchet (IAP) et Roland Triay (CPT)

This school, which is open to international students, has as objectives the reciprocal upgrade and the development of a multidisciplinary community on the research lines promoted by the CNRS. It will favour the transfer of methods/techniques and the development of a multidisciplinary community that is either connected or interested in the massive data processing and statistical analysis. It will train new generations of researchers, notably on the basis of the existing Planck community. They will thus be able to take up the many challenges of all kinds that these ambitious projects involve, on theoretical aspects, instrumental ones and analysis of massive and complex data. The competencies (already obtained) in the processing of data are of interest to other scientific communities which have already expressed their interest, which will lead to the creation of networks for exchanges and collaborations.

14h00 – 16h00, Amphi 5 - CPT

Differential calculus on h-deformed spaces

Basile HERLEMONT

Soutenance de thèse - Basile HERLEMONT

The ring Diff_h(n) of h-deformed differential operators of type A appears in the theory of reduction algebras. We construct the rings of generalized differential operators on the h-deformed vector space of gl-type. In contrast to the q-deformed vector space, where the ring of differential operators is unique, up to an isomorphism, the general ring of h-deformed differential operators Diff_h,σ(n) is labeled by a rational function σ in n variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system. We show that the center of Diff_h,σ(n) is a polynomial ring in n variables. We construct an isomorphism between certain localizations of Diff_h,σ(n) and the Weyl algebra Wn extended by n indeterminates. We present some conditions for the irreducibility of the finite dimensional Diff_h,σ(n)-modules. Finally, we show that finding analogue constructions for the ring Diff_h(n, N) of several copies of Diff_h(n) is a difficult task.

Agenda