Title: From Manin–Mumford to Dynamical Rigidity.Abstract:  In the early 1980s, Raynaud proved a theorem (the Manin–Mumford Conjecture) about the geometry of torsion points in abelian varieties, using number-theoretic methods.  Around the same time, and with completely different methods, McMullen proved a dynamical rigidity theorem for holomorphic maps on P1.  In recent work, joint with Myrto […]

Title: Characteristic classes of p-adic local systems.Abstract: A useful tool in studying vector bundles on topological spaces or algebraic varieties is characteristic classes in cohomology, such as Chern classes. For vector bundles equipped with a flat connection, Chern classes vanish in cohomology with rational coefficients, but such bundles have a non-trivial theory of secondary characteristic classes, […]

Title: Hodge symmetries of singular varieties.Abstract: The Hodge diamond of a smooth projective complex variety contains essential topological and analytic information, including fundamental symmetries provided by Poincaré and Serre duality. I will describe recent progress on understanding how much symmetry there is in the analogous Hodge–Du Bois diamond of a singular variety, and the concrete ways […]