Dynamics and topology of absolute period foliations

Karl Winsor (Harvard University)

Monday 17th January 16:00-17:00 Online + Maths 311B

Abstract

We will give an introduction to the absolute period foliation of a stratum of holomorphic 1-forms (or translation surfaces). Leaves of this foliation are navigated by moving zeros relative to each other while keeping the absolute periods fixed. We will show the absolute period foliation is ergodic in most cases, and we will 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. No prior familiarity with translation surfaces will be assumed.

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