Prof. Sebastian Heller (University of Tubingen)
November 17-18, 16-18 hr., Palazzo delle Scienze
Contact Stefano Montaldo for more information.
In these lectures I will talk about constant mean curvature (CMC) surfaces of higher genus in space forms from the integrable systems point of view. CMC surfaces are characterized by the harmonicity of their Gauss map and hence deliver an associated family of CMC surfaces (with periods). After recalling the general gauge theoretic description of CMC surfaces and their associated families, I will explain the recent spectral curve approach to CMC surfaces of higher genus. I will introduce a flow on the spectral data which turns out to be a powerful tool for a detailed study of the moduli space of CMC surfaces. Finally, I will report about numerical experiments and about the visualization of CMC surfaces. These lectures are partially based on joint work with Lynn Heller and Nicholas Schmitt.