Presentation
Many manifolds come equipped with a distinguished class of subvarieties: their special subvarieties. For instance:- locally symmetric spaces come with their totally geodesic subspaces.
- abelian varieties come with the (translates by torsion points of) their abelian subvarieties, (mixed) Shimura varieties with their Shimura subvarieties. More generally, complex quasi projective varieties endowed with a variation of (mixed) Hodge structures come with the irreducible components of their Hodge loci.
- strata of abelian differentials come with their affine invariant submanifolds.
Recent years saw a lot of activity around the following unifying principle: there is a natural dichotomy typical/atypical among special subvarieties; the typical special subvarieties should be numerous, while the atypical ones should be rare (Zilber-Pink philosophy).
The finiteness results build on various tools and ideas: Hodge theory, bi-algebraic geometry and functional transcendence, o-minimality, homogeneous and non-homogeneous dynamics. The goal of this workshop is to present these tools and results to a mixed audience, to identify the many similarities and to explore further these new fascinating interconnected phenomena.
Program, schedule, participants
ProgramParticipants
Schedule
Venue
All lectures will take place at the Villa del Grumello, Lake School of Advanced Studies
