We will give an introduction to the absolute period foliation of a stratum of holomorphic 1-forms, whose leaves are navigated by moving zeros relative to each other while keeping the absolute periods fixed. We will present some dynamical results that show the absolute period foliation is ergodic on the area-1 locus in most cases and that give explicit full measure sets of dense leaves. We will also address a related topological question of when two holomorphic 1-forms with the same absolute periods can be connected by a path of isoperiodic 1-forms. Our results suggest that a version of Ratner's orbit closure theorem may hold in this setting.
Speaker(s): Karl Winsor (Harvard)