On July 30, 2024, Dr. Marta Pieropan from Utrecht University will present a new version of the hyperbola method that is suitable to count rational points of bounded height on algebraic varieties. Anyone interested is welcome! The details of her talk are as follows:

Tuesday (30.07), 14:00 – 15:00, Room 403

Title: Rational points and Campana points on toric varieties and their subvarieties

Abstract: In joint work with Damaris Schindler we develop a new version of the hyperbola method for counting rational points of bounded height that generalizes the work of Blomer and Brüdern for products of projective spaces. The hyperbola method transforms a counting problem into an optimization problem on certain polytopes. For rational points on subvarieties of toric varieties, the polytopes have a geometric meaning that reflects Manin’s conjecture, and the same holds for counts of Campana points of bounded height. I will present our results as well as some general heuristics.