


Institute
of Mathematical Research 
Department
of Mathematics 
Department
of Mathematics and IMS 
Room 517, Meng Wah Complex, HKU
Equidistribution of Shimura Subvarieties
Professor Laurent Clozel
Abstract
Assume S is a Shimura variety
(essentially, an arithmetic quotient of a symmetric space). A conjecture of
André and Oort has the following consequence: if T_{n} is
a family of subvarieties of S, of the same type ("subShimura varieties"), there
should be a finite set (S_{m})
of subShimura varieties of S such
that each T is contained in one of
the S_{m} .
Ullmo and the speaker (and a further paper of Ullmo) prove this, essentially when all the subvarieties are of positive dimension. In turn this is
used in the proof, announced by Klingler and Yafaev, of the full AndréOort
conjecture.
I
will explain the results by Ullmo and myself, and the
ergodic method used in the proofs.
This meeting is hosted by the
All are Welcome 
Tea will be held in Room 516, Meng Wah Complex at