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 quasi-regular 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.