Geometric applications of Zilber-Pink
Prof. Gregorio Baldi
2024-04-24 14:00-15:30
MCM210&ZOOM
Speaker: Prof. Gregorio Baldi (CNRS)Time & Venue:
14:00-15:30 April 16 (Tuesday), April 17 (Wednesday), April 19 (Friday)
MCM110 & Online (Zoom ID: 3329836068 Password: mcm1234)
14:00-15:30 April 22 (Monday), April 24 (Wednesday)
MCM210 & Online (Zoom ID: 3329836068 Password: mcm1234)
Title: Geometric applications of Zilber-Pink
Abstract: Many manifolds M come naturally with a distinguished class of submanifolds (M_i)_i exhibiting a special behaviour. Examples include abelian varieties with sub-abelian varieties; Shimura varieties and more general period domains with sub-Shimura varieties and sub-period domains; and locally homogeneous spaces with totally geodesic sub-spaces. Given a submanifold S of M, one then obtains a distinguished class of special intersections S \cap M_i. The Zilber-Pink viewpoint suggests that the distribution behaviour of the special intersections can often be understood by simple dimension criteria.
We will present the general theory in its Hodge theoretic incarnation, as well as applications regarding representations of complex hyperbolic lattices and the distribution of orbit closures in strata of abelian differentials.
2024 Mini-course Outline:
Introduction to the completed Zilber-Pink viewpoint
Arithmeticity criteria for complex hyperbolic lattices
Superrigidity of rich representations
The distribution of the Hodge locus
A new proof of the geometric part of Zilber-Pink and further applications
