Joint equidistribution of arithmetic orbits, joinings, and rigidity of higher rank diagonalizable actions I

Joint equidistribution of arithmetic...diagonalizable actions I - Elon Lindenstrauss

Elon Lindenstrauss
Hebrew University of Jerusalem
March 2, 2015
An important theme in homogenous dynamics is that two parameter diagonalizable actions have much more rigidity than one parameter actions. One manifestation of this rigidity is rigidity of joinings of such actions. Joinings are an important concept in the study of dynamical systems, and allow detection of "hidden common denominator" of two (or more) dynamical systems. While one parameter diagonalizable actions on homogenous spaces have lots of joinings, for two parameter actions any measurable joining can be provided to be in fact of a very precise algebraic kind. I will present this joining rigidity theorem, and how it can be used to prove equidistribution statements of orbits of interest in arithmetic. These talks are based on joint work with M. Einsiedler.