Periods of Hypersurfaces via Effective Homology

Explore a 44-minute lecture on computing periods of hypersurfaces using effective homology techniques. Delve into the concept of period matrices for smooth complex projective varieties and their significance in encoding isomorphisms between singular homology and De Rham cohomology. Learn about a novel method for obtaining numerical approximations of periods for hypersurfaces, which relies on computing effective descriptions of homology. Discover how this approach is powerful enough to calculate periods for dense quartic K3 surfaces in three-dimensional projective space. Gain insights from Eric Pichon-Pharabod of Université Paris-Saclay and Inria Saclay as he discusses the potential of this method to recover algebraic invariants of varieties through precise numerical approximations, as demonstrated by Torelli-type theorems.