Hyperbolicity, Spring 2022
Professor A.J. de Jong, Columbia university, Department of Mathematics.
This semester the seminar is being organized by Akash Sengupta and myself.
Please email me if you are interested in being a part of this and want to be on the mailing list.
The seminar will be held on Friday mornings from 10:30 -- 12:00 in Room 507 in the math building at Columbia.
List of talks
- Introduction: Definitions, examples and basic results about different notions of hyperbolicity, their conjectural equivalence and overview of results.
- Analytic preliminaries: Ahlfors-Schwarz lemma, Jet differentials, Voisin, Debarre
- Hyperbolicity of subvarieties of Abelian varieties: Bloch’s theorem, Voisin, Theorem 1.18, Green, Kawamata
- Algebraic and analytic hyperbolicity of varieties with ample cotangent bundle, Examples and construction of such varieties Debarre, 3.4
- Algebraic and entire curves on surfaces of general type: Bogomolov’s theorem, Debarre, Section 7, Voisin, Theorem 2.6, Bogomolov,
- Hyperbolicity of hypersurfaces and their complements, Voisin, Section 3.1
- Calabi-Yau hypersurfaces. A geometric application of Nori's connectivity theorem: Clemens versus Lang for general hypersurfaces, Voisin, Section 3.2, Voisin
- Finiteness of the set of surjective morphisms onto algebraically hyperbolic varieties, via boundedness and grouplessness, Javanpeykar-Kamenova
- Strong Lang’s conjecture for subvarieties of abelian varieties, Faltings
- Finiteness of rational points for varieties with ample and globally generated cotangent bundle, Moriwaki
- Uniformity of rational points, Caporaso-Harris-Mazur
- The Erdős-Ulam problem and Lang's conjecture, Ascher-Braune-Turchet, Tao
- p-torsion monodromy of elliptic curves, pseudo-hyperbolicity properties of (X(p) x X(p))/SL_2(F_p), Bakker-Tsimmerman
- Integral points and Lang-Vojta conjecture, a generalization of Moriwaki's theorem Ascher-deVleming-Turchet: Theorem 1.6, Ascher-Turchet: Theorem 8.1
- Lang-Vojta for function fields, examples? Brief exposition and more references in Ascher-Turchet
List of meetings
- Feb 4. Akash Sengupta. Lecture I above.
- Feb 11. Akash Sengupta. Lecture II above.
- Feb 18. Johan de Jong. Lecture III above.
- Feb 25. Amal Mattoo. Lecture IV above.
- Mar 4. Noah Olander. Lecture V above.
- Mar 11. Nicolas Vilches Reyes. Lecture VI above.
- Mar 18. Spring break. No lecture.
- Mar 25. Patrixk lei. Lecture VII above.
- Apr 1. Morena Porzio. Lecture IX above.
- Apr 8. Kuan-Wen Chen. Lecture VIII above.
- Apr 15. Kevin Yaolin Chang. Lecture XI above.
- Apr 22. Akash Sengupta. The product theorem
- Apr 29.
List of survey articles
- On some problems of Kobayashi and Lang; algebraic approaches, Voisin
- Hyperbolic and Diophantine analysis, Lang
- Hyperbolicity of complex varieties, Debarre
- The Arithmetic and the Geometry of Kobayashi Hyperbolicity, Coskun
- The Lang-Vojta conjectures on projective pseudo-hyperbolic varieties, Javanpeyker
- Hyperbolicity of varieties of log general type, Ascher-Turchet
- Recent results on the Kobayashi and Green-Griffiths-Lang conjectures, Demailly