Typical and Atypical Intersections - Geometry, Dynamics, and Applications

Explore the geometric structures and symmetries of special submanifolds through this research seminar from the Institute for Advanced Study. Delve into the framework of unlikely intersections and functional transcendence as applied to abelian varieties, locally symmetric spaces, period domains, and strata of abelian differentials. Examine how this perspective advances understanding of non-arithmetic complex hyperbolic lattices and affine invariant submanifolds, complementing traditional dynamical approaches. Learn about the proof of the geometric Zilber–Pink conjecture and discover general results concerning the distribution of the Hodge locus, gaining insight into how these mathematical structures encode internal symmetries across various geometric spaces.