Abstract:
We will talk about the proof of Manin's conjecture on the asymptotic
density of rational points of bounded height for the special case of a compactification of
a semisimple algebraic group defined over a number field. The main tool is
the mixing property (or equivalently, the decay of matrix
coefficients) of the quasiregular representation of the associated Adele group.
No background in algebraic geometry or adeles will be assumed.
If time permits, I will also discuss a new approach to Manin's
conjecture based on Ratner's theory of unipotent flows.
