Mathematische Gesellschaft

Donnerstag, 02.02.2017

Christoph Bohle, Universität Tübingen

Differential Geometry and Integrable Systems (or why beautiful shapes are represented by beautiful formulae)


Many concepts from the theory of integrable PDEs appeared previously in classical differential geometry. However, the development of modern soliton theory took place independently of previous work in differential geometry and even today the strong connections between both topics are not widely known. I plan to explain a general conceptual approach for discussing such connections (by identifying geometric objects within the framework of the multi-component KP hierarchy). I will illustrate this mechanism in the example of curves and surfaces, but the underlying ideas are quite universal and apply in much more general situations.