Compactness and uniformity in number theoryMPIM

by Nuno Hultberg (Westlake University)

Monday Jul 6, 2026, 3:15 PM → 5:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

The Unterseminar

A continuous function from a compact space X to the real numbers that is positive at each point admits a uniform lower bound. Using the compactness theorem in logic allows us to apply this simple observation in a wide variety of settings. In Diophantine geometry the observation allows us to reduce uniform statements over the algebraic numbers to non-uniform results for arbitrary globally valued fields.