Computing linear relations between univariate integrals

The study of integrals of univariate algebraic functions (1-periods) provided
the impetus to develop much of algebraic geometry and transcendental number
theory. This old saga is now at a point of resolution. In 2022, Huber and
Wüstholz gave a "qualitative description" of all linear relations with
algebraic coefficients between 1-periods. New techniques for the determination
of symmetries of complex tori allow us to develop algorithms to explicate these
qualitative relations and to decide transcendence of 1-periods. This is a talk
for a general audience that describes the context of this subject and overviews
work-in-progress with Joël Ouaknine (MPI SWS) and James Worrell (Oxford).