Description
Orbit Closures as Atypical Intersections
We review the Hodge-theoretic characterization of orbit closures due to Filip. Using this characterization, we then explain how the theory of atypical intersections from Hodge theory naturally lets us classify such orbit closures as "typical" and "atypical". This classification recovers a finiteness theorem of Eskin, Filip and Wright for atypical orbit closures. If we have time, we explain how this finiteness can be made effective. Joint work with Greg Baldi.
