Time: 15:00-16:00, Monday, October 26, 2026
Venue: E14-301
Speaker: Paolo Dolce, ITS
Title: Kobayashi length bounds on bordered surfaces and generalized integral points on abelian varieties
Abstract: We prove square-root bounds for the Kobayashi length of loops avoiding finitely many points on a bordered Riemann surface. The proof combines local metric estimates with an averaging argument. Following the method of Parshin and Phung, we apply these bounds to generalized integral points on abelian varieties over complex function fields, obtaining improved counting estimates and linear height bounds. Under suitable geometric hypotheses on the divisor, this establishes a case of the geometric Lang–Vojta conjecture in its fixed-base, fixed-model form.
