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