Dirac operators were used in the context of Representation Theory by Parthasarathy in 1972, as invariant first order differential operators acting on sections of homogeneous vector bundles over symmetric spaces $G/K$ in order to obtain realizations of the discrete series representations of $G$.
In a series of lectures in 1997, Vogan introduced an algebraic analogue of Parthasarthy's Dirac...
Dans un travail récent avec Valentin Ovsienko, nous avons introduit des q-analogues des nombres rationnels. Il s’agit de fractions rationnelles à coefficients entiers s’obtenant naturellement par une approche combinatoire. Un remarquable phénomène de stabilisation permet d'étendre la q-déformation à tout nombre réel menant à des séries formelles à coefficients entiers. Si à l’origine des...
For a long time, by now, I have been working on geometries related to associative and non-associative algebras. First of all, I will discuss some aspects of associative structures, such as associative geometries, defined in work with M. Kinyon, https://arxiv.org/abs/0903.5441. Second, I will propose a framework of graded associative structures, following...
$SL(2,R)$ is an example of a hyperbolic locally compact group, i.e. a locally compact group that is Gromov hyperbolic with respect to the word metric associated with a compact generating set. This talk, based on joint work with Mehrdad Kalantar and Nicolas Monod, is devoted to the structure of hyperbolic locally compact groups that are of Type I. The Type I property formalizes the condition...
