Conformal Nets and Topological Modular Forms

Project Summary: Some mathematical notions can be described in both algebraic and geometric ways. The geometric descriptions are sometimes richer and can reveal hidden symmetries. K-theory is an example of a theory that has both and algebraic and geometric description. It links algebraic topology with geometry on curved spaces, to the mutual benefit of both disciplines. We believe that the notion of topological modular forms (TMF ) can play a similar role by connecting algebraic topology with geometry on loop spaces. The latter is a subject with many open questions, and it is strongly influenced by string theory.