Ziyang Gao


Professor (level W3), Leibniz University Hannover

I will move to UCLA in Fall 2024.


Email : ziyang.gao AT math.uni-hannover.de
Address : IAZD, Leibniz University Hannover, Welfengarten 1, 30167 Hannover, Germany.
Office : A412
Photo

Research Interests

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

Grants

My research is supported by ERC-Starting-Grant n. 945714 UnIntUniBd. Two working groups under this grant: Rational Points and Uniformity (2020-2021, IMJ-PRG, Paris), Adelic line bundles over quasi-projective varieties (2021-2022, Hannover, joint with Basel).

Publications and preprints

The documents here may be slightly different from the published versions.
  1. (with Shouwu Zhang) Heights and periods of algebraic cycles in families, preprint 2024.
  2. Compte-rendu: Bigness of the tautological line bundle and degeneracy loci in families of abelian varieties, 2024.
  3. (with Emmanuel Ullmo and Andrei Yafaev) Bi-Q -structure on Hermitian symmetric spaces and quadratic relations between CM periods, preprint 2024.
  4. (with Philipp Habegger) The Relative Manin-Mumford Conjecture, preprint 2023.
  5. (with Philipp Habegger) Degeneracy loci in the universal family of abelian varieties, accepted to Journal of Number Theory (JNT Prime), Proceedings of the Second JNT Biennial Conference 2022, online 2024, doi.org/10.1016/j.jnt.2024.05.015.
  6. (with Tangli Ge and Lars Kühne) The Uniform Mordell-Lang Conjecture, preprint 2021.
  7. Survey: Recent developments of the Uniform Mordell-Lang Conjecture, preprint 2021.
  8. (with Bruno Klingler) The Ax-Schanuel conjecture for variations of mixed Hodge structures, Math. Ann., vol. 388, p. 3847-3895, 2024 (published online in 2023).
  9. (with Vesselin Dimitrov and Philipp Habegger) A consequence of the relative Bogomolov conjecture, Journal of Number Theory (JNT Prime), vol. 230 (Proceedings of the First JNT Biennial Conference 2019), p. 146-160, 2022.
  10. (with Vesselin Dimitrov and Philipp Habegger) Uniformity in Mordell-Lang for curves, Annals of Mathematics, vol. 194, p. 237-298, 2021.
  11. (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.
  12. Generic rank of Betti map and unlikely intersections, Compositio Mathematica, vol. 156, p. 2469-2509, 2020. Erratum
  13. (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.
  14. Mixed Ax-Schanuel for the universal abelian varieties and some applications, Compositio Mathematica, vol. 156, p. 2263-2297, 2020.
  15. (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.
  16. 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.
  17. (with Philipp Habegger) Heights in families of abelian varieties and the Geometric Bogomolov Conjecture, Annals of Mathematics, vol. 189, p. 527-604, 2019.
  18. 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.
  19. About the mixed André-Oort conjecture: reduction to a lower bound for the pure case, Comptes rendus Mathématiques, vol. 354, p. 659-663, 2016.
  20. 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.
  21. 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) defense on June 28, 2021 Distribution of points on varieties: various aspects and interactions. Here are the slides.
  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.