Abstract: Since the middle of the 19th century surface theory has attracted strong interest by world-leading mathematicians, with classical surface geometers such as Gauss, Darboux, and Bianchi studying local properties and transformations whereas modern contributions add global aspects and applications in e.g. Computer Graphics, Machine Learning, and Architecture. Despite this, even now the theory lacks a depth of global results and non-trivial examples when compared to the powerful algebraic geometric theory of complex curves. In this talk, I will explain how Quaternionic Holomorphic Geometry (QHG) extends results of this theory of complex curves to surface theory by considering conformal surfaces as the holomorphic objects of the theory. I will discuss recent results on the integrable systems of minimal, CMC, and isothermic surfaces to illustrate the power of QHG in these applications.

Contact Marcel Bökstedt marcel@math.au.dk, for Zoom details.