Institute of Mathematical Research HKU	Department of Mathematics HKUST	Department of Mathematics and IMS CUHK

Hong Kong Geometry Colloquium

April 13, 2006 (Thursday), 4:00 – 5:00pm

Room 517, Meng Wah Complex, HKU

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Equidistribution of Shimura Subvarieties

Professor Laurent Clozel

Université de Paris-Sud

Orsay, France

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 ("sub-Shimura varieties"), there should be a finite set (S_m) of sub-Shimura 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 André-Oort conjecture.

I will explain the results by Ullmo and myself, and the ergodic method used in the proofs.

This meeting is hosted by the Institute of Mathematical Research, HKU.

All are Welcome

Tea will be held in Room 516, Meng Wah Complex at 3:40pm