## EVENT DETAILS AND ABSTRACT

**Number Theory**
**Title:** Recent developments on the AndrĂ©-Oort conjecture

**Speaker:** Ziyang Gao

**Speaker Info:** IAS

**Brief Description:**

**Special Note**:

**Abstract:**

The AndrĂ©-Oort conjecture predicts that any subvariety of a mixed Shimura variety containing a Zariski dense subset of special points is again a moduli space of some mixed Hodge structures with some Hodge tensors. An interesting example is when the ambient mixed Shimura variety is the universal abelian variety, in which case special points are precisely the points corresponding to torsion points on CM abelian varieties. This conjecture was reduced to a lower bound for the size of Galois orbits of special points by a series of work (Klingler-Ullmo-Yafaev, Pila-Tsimerman, Gao) and hence proved for mixed Shimura varieties of abelian type by the recent work of Tsimerman and Yuan-Zhang/Andreatta-Goren-Howard-Pera. In the proof, a transcendental and a distribution theorem (Ax-Lindemann and its corollary) of independent interest were proved. In my talk I will explain this conjecture and sketch its proof. In particular I will explain the very recent result of Tsimerman about how to prove the lower bound using the Colmez conjecturein average.

**Date:** Monday, October 19, 2015

**Time:** 4:00PM

**Where:** Lunt 107

**Contact Person:** Yifeng LIu

**Contact email:** liuyf@math.northwestern.edu

**Contact Phone:**

Copyright © 1997-2024
Department of Mathematics, Northwestern University.