Greg Baldi : Typical vs. Atypical Intersections and Applications

Posted by Dhruv Mubayi , part of the Departmental Colloquium.

At

Nov. 7, 2025, 3 p.m.

In

636 SEO

Abstract

Many geometric spaces come equipped with a natural collection of special submanifolds that reflect their internal symmetries. Examples include abelian varieties with their sub-abelian varieties, locally symmetric spaces with totally geodesic subspaces, period domains with sub–period domains, and strata of abelian differentials with affine invariant submanifolds. In recent years, significant progress has been made in understanding such structures through the lens of unlikely intersections and functional transcendence. I will outline the general framework of variations of Hodge structures and period domains, and explain how the so-called completed Zilber–Pink philosophy provides a unifying way to describe the qualitative behaviour of these special loci. This perspective reveals deep connections between arithmetic geometry, Hodge theory, and dynamical systems.