Equidistribution problems and semisimple Lie groups

California Institute Of Technology, Pasadena CA

Investigators

Abstract

Title: Equidistribution problems and semisimple Lie groups The investigator, in several joint works with W. T. Gan and A. Eskin, has exploited methods from harmonic analysis and ergodic theory to understand the equidistribution phenomenon of integer representations of invariant polynomials. The investigator proposes to continue her study on equidistribution questions on homogeneous spaces of semisimple Lie groups, especially those connected with problems in number theory and geometry. For example, the problem of understanding compact maximal flats in Riemannian symmetric space or orbits of lattices in various homogeneous spaces of Lie groups are of interest. The application of ergodic theory and the representation theory of semisimple Lie groups in number theory is one of newly discovered tools in modern mathematics. The methods, when applicable, turn out to be very powerful and solve some of the important problems which pure number theoretic methods cannot deal with. The investigator is interested in the problems at this intersection and hopes to develop further tools to deal with them.