Arithmetic and Diophantine Geometry, via Ergodic Theory and o-minimality

Session

Afternoon Chair: Pascal Autissier

9 sept. 2025, 14:00

Centre de conférences Marilyn et James Simons (Le Bois-Marie)

8. Baily–Borel Compactifications of Period Images and the b-Semiampleness Conjecture

Benjamin Bakker (Univ. of Illinois, Chicago)

09/09/2025 14:00

We address two questions related to the semiampleness of line bundles arising from Hodge theory. First, we prove there is a functorial compactification of the image of a period map of a polarizable integral pure variation of Hodge structures for which a natural line bundle extends amply. This generalizes the Baily--Borel compactification of a Shimura variety, and for instance produces...

9. Applications of Unlikely Intersections to Integral Geometry

David Urbanik (IHES)

09/09/2025 15:15

We explain how a theory of infinitesimal period maps can be used to "transfer" Hodge-theoretic unlikely intersection results from characteristic zero to positive characteristic for sufficiently large primes p. We survey several results of this type and give an idea of the methods used to prove them. Partially joint work with Ziquan Yang.

10. A Tribute to Emmanuel's Contributions to the Zilber–Pink Conjecture

Gregorio Baldi (IHES)

09/09/2025 16:45

We will survey several of Emmanuel’s influential results over the past two decades concerning the André–Oort conjecture and the broader Zilber–Pink conjecture. Beginning with the framework of Shimura varieties, we will gradually transition toward more general settings involving arbitrary variations of Hodge structures. This shift marks a movement from the arithmetic study of CM points to a...