11 Luglio, 2016 16:30

Lezioni Leonardesche

DIAGONAL FLOWS, JOININGS AND ARITHMETIC

Elon Lindenstrauss, Hebrew University of Jerusalem

Aula Chisini, via Saldini 50

Arithmetic quotients of algebraic groups such as the space of unit volume lattices in R^n can be studied fruitfully from many directions and contain deep and subtle arithmetic information. Homogeneous dynamics studies these spaces by considering the action of a subgroup of the algebraic group on such a quotient. Of particular interest is the action of multiparameter diagonal groups: these display remarkable rigidity properties that are absent in the context of one parameter diagonalizable group actions.

One aspect of this rigidity is joining rigidity: under suitable conditions, knowing that an orbit of a multiparameter diagonalizable group in a product of two arithmetic quotients is equidistributed in each one of these quotients individually implies joint equidistribution.

I would explain this phenomena as well as some arithmetic consequences.