Geometry Seminar


Adelic equidistribution of arithmetic quotients


Professor Laurent Clozel

Université de Paris-Sud
Orsay, France





Assume S = G/G is an arithmetic quotient of a Lie group G defined over Q. If H is a subgroup of G defined over Q, arithmetic quotients of H define naturally measures on S. If Hn is a strict sequence of G in the sense of Algebraic geometry, one should expect the measures to converge to the natural, invariant, measure on G/G.

I will describe some cases where this follows from Ratner's theory. In some cases, however, this is false. Ullmo and I have proposed an adelic reformulation of the conjecture. For sequences of tori in SL(2) - over a number field - the new conjecture is true, as a consequence of deep results in Analytic Number theory. If time allows, I will describe the relation with problems concerning Shimura varieties.



April 11, 2006 (Tuesday)


2:00 – 3:00pm


Room 517, Meng Wah Complex, HKU




All are welcome