Speaker: Emre Sertoz.
Date: 10:30 17/07/2020
Abstract: Kontsevich--Zagier periods form a natural number system that extends the algebraic numbers by
adding constants coming from geometry and physics. Because there are countably many periods, one would
expect it to be possible to compute effectively in this number system. This would require an effective
height function and the ability to separate periods of bounded height, neither of which are currently
possible.
In this talk, we introduce an effective height function for periods of quartic surfaces
defined over algebraic numbers. We also determine the minimal distance between periods of bounded
height on a single surface. We use these results to prove heuristic computations of Picard groups
that rely on approximations of periods. Moreover, we give explicit Liouville type numbers that can
not be the ratio of two periods of a quartic surface. This is ongoing work with Pierre Lairez (Inria, France).