Speaker: Sergei Yakovenko, Weizmann Institute, Rehovot, Israel
Date: 10:30 09/04/2021
Title:How transcendental are Periods?
Abstract: Periods (integrals of rational 1-forms over algebraic 1-cycles) in general are transcendental
functions of the relevant parameters, since even a single integration destroys algebraicity.
However, it turns out that their behavior (in particular, the number of isolated zeros when restricted on
one-dimensional lines in the parameter space) is similar to that of algebraic functions (in particular,
the number of zeros is explicitly bounded from above). This implies an explicit upper bound for an infinitesimal
flavor of the Hilbert 16th problem. The main engine of the proof is a subtle difference between systems of
first order linear ordinary differential equations on the projective line and linear equations of higher order
with rational coefficients.