Diagonal flows, joinings and arithmetic

Speaker
Elon Lindenstrauss
Date
30/04/2017 - 15:00 - 14:00Add to Calendar 2017-04-30 14:00:00 2017-04-30 15:00:00 Diagonal flows, joinings and arithmetic 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, this rigidity implies that 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. Colloquium Room אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Colloquium Room
Abstract
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, this rigidity implies that 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.

Last Updated Date : 23/04/2017