Seminar on Complex Analysis and Complex Geometry - Spring 2026

Friday, February 27, 2026, 10:30-11:30, room PGH 648

Title: A New Diophantine Approximation on Surfaces and Degeneracy of Integral Points

Speaker: Zheng Xiao, University of Colorado, Boulder

Abstract: After Mordell’s conjecture for curves was proved by Faltings, attentions turn to the distribution of rational and integral points on higher dimensional varieties, which is encoded in the celebrated Vojta’s conjecture. Along this line we proved a subspace type inequality, improving the result of Ru-Vojta, on surfaces. Meanwhile, we obtain a sharp criterion of when some certain surfaces admit a non Zariski-dense set of integral points. If time permits, I will also discuss possible applications and higher dimensional generalizations. This is a joint with K. Huang, A. Levin.