Email: kwinsor at math dot harvard dot edu
I am a graduate student in mathematics at Harvard, advised by Curt McMullen.
My research interests include group actions and foliations on moduli spaces, arithmetic properties of pseudo-Anosov homeomorphisms, and dynamics of billiards and interval exchanges.
Title: Dense absolute period leaves and relative period geodesics (2021), draft available upon request
Abstract: We give explicit examples of dense leaves of the absolute period foliation, and dense complex relative period geodesics, in the area-1 locus of every connected component of every stratum of holomorphic 1-forms with multiple zeros. Our examples arise from holomorphic 1-forms with periodic horizontal and vertical foliations. We also prove the existence of dense relative period geodesics in these loci.
Title: Dynamics of the absolute period foliation on strata of holomorphic 1-forms (2021), draft available upon request
Abstract: We show that the absolute period foliation on the area-1 locus of a connected stratum of holomorphic 1-forms with multiple zeros is ergodic. We give an explicit full measure set of dense leaves. With this set, the space of holomorphic 1-forms representing a given cohomology class is connected. We also show that the space of holomorphic 1-forms in a stratum representing a given cohomology class can simultaneously have positive dimension and infinitely many connected components.