Ziyang GAO


Chargé de Recherche (junior researcher, with tenure),
CNRS and Institut de Mathématiques de Jussieu-Paris Rive Gauche (Paris).


Email : ziyang.gao AT imj-prg.fr
Address : 4 place Jussieu, 75005 Paris, France.
Office : 15-25-403
Photo

Research Interests

My research interests focus on arithmetic geometry. I work on Shimura varieties (both pure and mixed), abelian varieties and diophantine geometry.

Publications and preprints

The documents here may be slightly different from the published versions.
  1. (with Vesselin Dimitrov and Philipp Habegger) A consequence of the relative Bogomolov conjecture, preprint 2020.
  2. (with Vesselin Dimitrov and Philipp Habegger) Uniformity in Mordell-Lang for curves, preprint 2020.
  3. (with Vesselin Dimitrov and Philipp Habegger) Uniform bound for the number of rational points on a pencil of curves, IMRN, 2019, doi.org/10.1093/imrn/rnz248.
  4. Generic rank of Betti map and unlikely intersections, accepted to Compositio Mathematica.
  5. (with Serge Cantat, Philipp Habegger and Junyi Xie) The Geometric Bogomolov Conjecture, accepted to Duke Math. J.
  6. Mixed Ax-Schanuel for the universal abelian varieties and some applications, accepted to Compositio Mathematica.
  7. (with Rafael von Känel and Lucia Mocz) Faltings Heights and L-functions, in Arithmetic and Geometry: Ten Years in Alpbach edited by Gisbert Wüstholz and Clemens Fuchs, Annals of Mathematics Studies 202, Princeton U. Press.
  8. Appendix to The Betti map associated to a section of an abelian scheme (Yves André, Pietro Corvaja and Umberto Zannier), Inventiones mathematicae, 2020, doi.org/10.1007/s00222-020-00963-w.
  9. (with Philipp Habegger) Heights in families of abelian varieties and the Geometric Bogomolov Conjecture, Annals of Mathematics, vol. 189, p. 527-604, 2019.
  10. Enlarged mixed Shimura varieties, bi-algebraic system and some Ax type transcendental results, Forum of Mathematics, Sigma, vol. 7, 2019, e16, doi.
    - Bi-algebraic system on the universal vectorial extension Oberwolfach report No. 21, 2016.
  11. About the mixed André-Oort conjecture: reduction to a lower bound for the pure case, Comptes rendus Mathématiques, vol. 354, p. 659-663, 2016.
  12. A special point problem of André-Pink-Zannier in the universal family of abelian varieties, Ann. Sc. Norm. Super. Pisa Cl. Sci., vol. XVII, p. 231-266, 2017.
  13. Towards the André-Oort conjecture for mixed Shimura varieties: the Ax-Lindemann theorem and lower bounds for Galois orbits of special points, Journal für die reine und angewandte Mathematik (Crelle), vol. 732, p. 85-146, 2017 (published online in March 2015).

Miscellaneous

Dissertations

  1. PhD defense on November 24, 2014. Thesis title The mixed Ax-Lindemann theorem and its applications to the Zilber-Pink conjecture. Supervisors: Emmanuel Ullmo and Bas Edixhoven.

Teaching

  1. Click here for past courses.

Links :

    Seminars : Ressources :