Adelic equidistribution of arithmetic quotients
Professor
Laurent Clozel
Abstract
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 H_{n}_{ }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.
Date: 

Time: 

Place: 
Room 517, Meng Wah Complex, HKU 

All are welcome 
