Rich representations and superrigidity
Abstract We investigate and compare applications of the Zilber–Pink conjecture and dynamical methods to rigidity problems for arithmetic real and complex hyperbolic lattices. Along the way, we obtain new general results about reconstructing a variation of Hodge structure from its typical Hodge locus that may be of independent interest. Applications to Siu’s immersion problem are also discussed, the most general of which only requires the hypothesis that infinitely many closed geodesics map to proper totally geodesic subvarieties under the immersion.
Authors
- Gregorio Baldi (ORCID: https://orcid.org/0000-0001-6703-7164)
- Emmanuel Ullmo
- Matthew Stover (ORCID: https://orcid.org/0000-0002-4423-6176)
- Nicholas Miller (ORCID: https://orcid.org/0000-0002-0913-5011)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Université Sorbonne Nouvelle (FR)
- Sorbonne Université (FR)
- Temple University (US)
- Institut des Hautes Études Scientifiques (FR)
- University of Oklahoma (US)
Publication Details
- Journal
- Ergodic Theory and Dynamical Systems
- Published
- 2025-01-27
- DOI
- https://doi.org/10.1017/etds.2024.136
- Primary Topic
- Advanced Topology and Set Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Division of Mathematical Sciences