DOCUMENTA MATHEMATICA, Extra Volume ICM II (1998), 539-552

Alex Eskin

Title: Counting Problems and Semisimple Groups

Some natural counting problems admit extra symmetries related to actions of Lie groups. For these problems, one can sometimes use ergodic and geometric methods, and in particular the theory of unipotent flows, to obtain asymptotic formulas. We will present counting problems related to diophantine equations, diophantine inequalities and quantum chaos, and also to the study of billiards on rational polygons.

1991 Mathematics Subject Classification: Primary 11J25, 22E40

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