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General Research Interests

Currently we subdivide our research interests into four domains as follows (the order is quite arbitrary):

  • Applications of number theory, in particular, of elliptic modular forms, in quantum field theory and in the theory of vertex operator algebras. Of course, we are also interested in automorphic forms in general.
  • Computation of automorphic forms: finding algorithms for such computations and also the implementations of these. This is closely connected to the project MODI (see below).
  • Finding (and specifying) absolute bound for algebro-arithmetic objects like regulators of number fields, heights on curves, Mahler mesures of polynomials and the like.
  • Mahler measures as special values of L-functions. This relation was discovered by Boyd and Smith almost 20 years ago, and was reinterpreted recently by Deninger with subsequent articles of Boyd and Villegas. Thomas Calvo is currently investigating more closely the case of Mahler mesures of polynomials in one variable under the point of view of Deninger, i.e. reinterpreting these measures as periods of suitable motives.

We would like to emphasize that we are, in addition, open to all kind of interdisciplinary activities and very much willing to extend our list of domains of interest into such directions.


MODI

In this long term project we try to set up a sort of web encyclopedia on automorphic forms. This is based on precomputed data and on cgi-scripts which manage real time computing on demand. Contributions from authors from other institutions are welcome and even desired. A first (and still very modest) version of modi is already available.


Conferences organized or coorganized by our group


International Workshop on Jacobi Forms and Applications ( May 7 to May 11, 2007 at the Centre Internatonale de Rencontres Mathématiques in Luminy near Marseille)

See the CIRM site for more details.


Workshop on Automorphic Forms (June 6, 2007, Siegen)

This international workshop will be organized in Siegen as part of the joint Seminar on Autmorphic Forms Aachen- Köln - Lille - Siegen, which started in 2003. The program is not yet available.


International Workshop on L-functions and modular forms (July 30 to August 3, 2007 at the American Institute of Mathematics, Palo Alto, California)

More information can be found on the AIM site


Workshop on Automorphic Forms (February 8, 2006, Siegen)

This international workshop was organized in Siegen as part of the joint Seminar on Autmorphic Forms Aachen- Köln - Lille - Siegen, which started in 2003. Poster and Photos are available.


Workshop on Automorphic Forms (January 12, 2005, Siegen)

This international workshop was organized in Siegen as part of the joint Seminar on Autmorphic Forms Aachen- Köln - Lille - Siegen, which started in 2003. Poster and Photos are available.


Workshop on Automorphic Forms (January 21, 2004, Siegen)

This international workshop was organized in Siegen as part of the Joint Seminar on Autmorphic Forms Aachen- Köln - Lille - Siegen, which started in 2003. Poster and Photos are available.


Conference on Jacobi Forms and Applications (September 24 - 28, 2001, Luminy)

Together with Prof. Valery Gritsenko (Lille) we organized an international conference on newer trends in the theory of Jacobi forms, and in particular on applications of Jacobi forms in physics (vertex operator algebras), in geometry (elliptic genera, modular varieties of surfaces) or in lattice and coding theory. For details see the special page dedicated to this meeting.