Arithmetic and Diophantine Geometry, via Ergodic Theory and o-minimality

Session

Morning Chair: Umberto Zannier

11 sept. 2025, 09:30

Centre de conférences Marilyn et James Simons (Le Bois-Marie)

14. A Quantitative Version of the Uniform Mordell Conjecture

Xinyi Yuan (BICMR, Peking Univ.)

11/09/2025 10:00

The celebrated Mordell conjecture proved by Faltings asserts that the number of rational points on a curve of genus greater than one over a number field is finite. A deep uniform upper bound on the number of rational points follows from Vojta's inequality and the recent works of Dimitrov-Gao-Habegger and Kuhne. In this talk, I will introduce an explicit version of this uniform bound. This is a...

15. Heights of Ceresa and Gross—Schoen Cycles

Shouwu Zhang (Princeton Univ.)

11/09/2025 11:15

In this talk, I will survey recent work on the heights of Gross—Schoen and Ceresa cycles, as well as their relation to the triple product L-series.