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 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.
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Room 517, Meng Wah Complex, HKU |
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All are welcome |
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