Separation of periods of quartic surfaces

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 joint work with Pierre Lairez (Inria, France).

Zoom Online Meeting ID: 919 6497 4060
For password see the email or contact Pieter Moree (moree@mpim...).