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
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NEW: Postdoc Positions

There are 2 open postdoc positions funded by the ERC-Starting Grant 945714: Unlikely Intersection and Uniform Bounds for Points. Click here for more details.

Research Interests

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

Working Group 2020-2021: Rational Points and Uniformity

Publications and preprints

The documents here may be slightly different from the published versions.
  1. Survey: Recent developments of the Uniform Mordell-Lang Conjecture, preprint 2021.
  2. (with Bruno Klingler) The Ax-Schanuel conjecture for variations of mixed Hodge structures, preprint 2021.
  3. (with Vesselin Dimitrov and Philipp Habegger) A consequence of the relative Bogomolov conjecture, preprint 2020.
  4. (with Vesselin Dimitrov and Philipp Habegger) Uniformity in Mordell-Lang for curves, preprint 2020, accepted to Annals of Mathematics.
  5. (with Vesselin Dimitrov and Philipp Habegger) Uniform bound for the number of rational points on a pencil of curves, IMRN, vol. 2021, p. 1138-1159, 2021 (published online in December 2019), doi.org/10.1093/imrn/rnz248.
  6. Generic rank of Betti map and unlikely intersections, Compositio Mathematica, vol. 156, p. 2469-2509, 2020. Erratum
  7. (with Serge Cantat, Philipp Habegger and Junyi Xie) The Geometric Bogomolov Conjecture, Duke Math. J., vol. 170, p. 247-277, 2021. doi:10.1215/00127094-2020-0044.
  8. Mixed Ax-Schanuel for the universal abelian varieties and some applications, Compositio Mathematica, vol. 156, p. 2263-2297, 2020.
  9. (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.
  10. Appendix to The Betti map associated to a section of an abelian scheme (Yves André, Pietro Corvaja and Umberto Zannier), Inventiones mathematicae, vol. 222, pp. 161-202, 2020.
  11. (with Philipp Habegger) Heights in families of abelian varieties and the Geometric Bogomolov Conjecture, Annals of Mathematics, vol. 189, p. 527-604, 2019.
  12. 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.
  13. About the mixed André-Oort conjecture: reduction to a lower bound for the pure case, Comptes rendus Mathématiques, vol. 354, p. 659-663, 2016.
  14. 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.
  15. 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. HDR (Habilitation à diriger les recherches) Distribution of points on varieties: various aspects and interactions.
  2. 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 :