Roever Lecture/Colloquium: Integrable Surface Geometry: Old and New

Abstract: The mid 1980s saw an influx of ideas from mathematical physics and (algebro-geometric) integrable systems in the study of special surfaces in 3-space, including minimal, constant mean curvature, and Willmore surfaces. These methods ultimately allowed the classification of all harmonic 2-tori in symmetric spaces of compact type. Over the past 10 years, significant inroads have been laid to extend this theory from tori to higher genus surfaces. The new ideas needed came from the theory of Higgs bundles, meromorphic connections, and loop group/algebra factorizations. Results, previously only accessible via hard PDE analysis, are now obtainable from elementary implicit function theorems. These yield more detailed results about quantities such as areas, enclosed volumes, and first Laplace eigenvalues of compact minimal surfaces in the 3-sphere. This talk is aimed at a general mathematical audience and basic concepts will be illustrated by computer generated images and video clips.

Host: Charles Ouyang

Tea Reception in Cupples I, Room 200 (Lounge) at 3:00 pm before the lecture