Speaker: Masha Vlasenko
Date: 10:30 06/11/2020
Title: Frobenius constants of differential equations
Abstract: Given an ordinary differential operator with a reflection type singularity at t=c, Frobenius constants describe
variation around c of Frobenius solutions defined near another regular singularity t=c'. These numbers often appear to be
interesting arithmetic constants. For example, an interpretation of ApĂ©ry's irrationality proof shows that zeta(3) is a
Frobenius constant attached to a Picard--Fuchs differential equation of a family of hypersurfaces.
In the joint work with Spencer Bloch we show that, quite generally, the generating series of Frobenius constants is a
Mellin transform of a solution of the adjoint differential operator. This peculiar property explains why Frobenius
constants of geometric differential operators are periods.