# Toroidal Soap Bubbles: Constant Mean Curvature Tori in $S^3$ and $R^3$

 Members' Seminar Topic: Toroidal Soap Bubbles: Constant Mean Curvature Tori in $S^3$ and $R^3$ Speaker: Emma Carberry Affiliation: University of Sydney Date: Monday, April 14 Time/Room: 2:00pm - 3:00pm/S-101 Video Link: http://video.ias.edu/members/2014/0414-EmmaCarberry

Constant mean curvature (CMC) tori in $S^3$, $R^3$ or $H^3$ are in bijective correspondence with spectral curve data, consisting of a hyperelliptic curve, a line bundle on this curve and some additional data, which in particular determines the relevant space form. This point of view is particularly relevant for considering moduli-space questions, such as the prevalence of tori amongst CMC planes. I will address these periodicity questions for the spherical and Euclidean cases, using Whitham deformations, which I will explain.