Frobenius constants for families of elliptic curves

Periods are complex numbers given as values of integrals of algebraic functions defined over domains, bounded by algebraic  equations and inequalities with coefficients in Q. In this talk, we will deal with a class of periods, Frobenius constants, arising as  matrix entries of the monodromy representations of certain geometric differential operators. More precisely, we will consider seven  special Picard - Fuchs type second order linear differential operators corresponding to families of elliptic curves. Using periods  of modular forms, we will witness some of these Frobenius constants in terms of zeta values. This is a joint work with Masha  Vlasenko.