Counting and Equidistribution on homogeneous spaces

Brown University, Providence RI

Investigators

Abstract

DMS-0629322 Hee Oh The proposal concerns four projects regarding the distribution of geometric and arithmetic objects on homogeneous spaces of Lie groups. They are equidistribution of Hecke correspondence, counting rational points of bounded height, distribution of rational points with given denominator and distribution of values of irrational forms. They propose to use techniques from various different fields such as harmonic analysis, dynamics of group actions, ergodic theory, automorphic forms of semisimple algebraic groups in order to prove (or disprove) the equidistribution of densely distributed objects arising in number theoretic and geometric situation. One of big achievements in modern mathematics is the use of ergodic theory, dynamics of homogeneous spaces, arithmetic geometry and automorphic forms in solving long standing open problems in number theory. The proposed projects are focused on establishing further these connections between different disciplines of mathematics.