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Cocycles and modular forms

Startdatum: 07.05.2019 - 16:00
Enddatum: 07.05.2019 - 17:30
Adresse: MZH 6210
Organisator/Ansprechpartner: Prof. Jens Rademacher, Prof. Christine Knipping, (0421) 218-63745, (0421) 218-63721
  • Prof. Don Zagier / Max Plank Institut für Mathematik, Bonn

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 socalled
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