The APDE seminar on Monday, 12/1, will be given by Mingfeng Chen (UW Madison) in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PDT. To participate, please email Adam Black (adamblack@berkeley.edu).

Title: Rational points near space curves

Abstract: How many rational points with a bounded denominator lie in a small neighborhood of a given manifold? This fundamental question in Diophantine approximation connects to dynamics, number theory, and harmonic analysis, with applications to problems like Khinchin’s theorem for manifolds and the dimension growth conjecture.
In this talk, I will present new results that establish the main conjecture for the case of space curves. This is joint work with A. Seeger, R. Srivastava and N. Technau.