Description
The period matrix of a smooth complex projective variety encodes the
isomorphism between its singular homology and its algebraic De Rham cohomology.
Numerical approximations with sufficient precision of the entries of the period matrix allow
to recover some algebraic invariants of the variety. Such approximations can be obtained
from an effective description of the homology of the variety, which itself can be obtained
from the monodromy representation associated to a generic fibration. I will describe
methods to compute periods to several hundreds digits of certified precision, and
showcase implementations and applications, in particular to computation of the Picard
rank of certain K3 surfaces appearing in Feynman integrals.