I will begin by reviewing the classical and very beautiful theorem of Eichler and Shimura that reinterprets modular forms in terms of 1-cocycles, and then show how one can also associate cocycles to more general "nearly modular" objects, like Eisenstein series of odd weight. This leads to a new and much simpler proof of an earlier joint result with Roelof Bruggeman and John Lewis associating cocycles in an appropriate cohomology group to so-called Maass wave forms. Another instance of the same idea, which will be described very briefly if time permits, is the construction of new knot invariants in  ongoing work with Stavros Garoufalidis and Rinat Kashaev. No prior knowledge is assumed; in particular, we will review from scratch the definitions of cocycles, modular forms, Eisenstein series, and Maass forms, giving examples in each case.

Einladung von Prof. Anke Pohl