Lille, 03.05.2017, le séminaire franco-allemand

[Valéry Gritsenko]

50th Seminar Aachen-Bonn-Köln-Lille-Siegen on Automorphic Forms
University Lille 1, May 3, 2017

Organizers: K. Bringmann, J. Bruinier, V. Gritsenko, A. Krieg, P. Moree,
G. Nebe, N-P. Skoruppa, S. Zwegers

USTL, Cité Scientifique Lille 1, Villeneuve d'Ascq
Bat. M3, la salle Duhem

14h00 ? 14h50 Emmanuel ROYER (Clermont-Ferrand)
Poisson structures, quasimodular forms & Jacobi forms.

15h00 ?15h50 Evgeny FERAPONTOV (Loughborough University, UK)
Dispersionless integrable systems and modular forms.

15h50?16h30 Coffee break

16h30?17h20 Gaetan Chenevier (Laboratoire de mathématiques d'Orsay)
On level 1 modular forms of small weights.

17h30?18h20 Nils-Peter Skoruppa (U. Siegen) T.B.A.

18h30 Buffet (in the building M2)

This is the 50th meeting of the joint French-German seminar on
automorphic forms. For further information concerning this meeting
please send an email to Valery.G...@math.univ-lille1.fr
For the previous meetings see
http://www.matha.rwth-aachen.de/en/forschung/abkls/

*********ABSTRACTS:

Emmanuel Royer
Poisson structures, quasimodular forms & Jacobi forms.

The sequence of Rankin-Cohen brackets is a formal deformation of the
algebra of modular forms. In recent works with F. Dumas and with Y.
Choie, F. Dumas & F. Martin, we construct formal deformations of the
algebras of quasi modular forms and weak Jacobi forms. A first step in
this description is a complete description of the Poisson structures on
these algebras.

Evgeny Ferapontov
Dispersionless integrable systems and modular forms.

In this talk I will give a review of several problems in the theory of
dispersionless integrable systems where modular forms occur naturally.
This includes the classification of first-order integrable Lagrangians
and second-order quasilinear PDEs.

Gaetan Chenevier
On level 1 modular forms of small weights.

I will show that, up to twist and action of GL(n,R), there are only 11
cuspidal modular eigenforms for GL(n,Z) all of whose "weights" are integers
in the range [0,22] (the positive integer n being arbitrary). For
instance, the constant function for n=1, and the classical cuspforms
of weight 12, 16, 18, 20 and 22 for n=2, define 6 of those 11, and I
will explain that there are none for n>4. I will give several
applications of this result, such as a proof "without any lattice
computation" that there are exactly 24 isometry classes of even
unimodular lattices in rank 24 (Niemeier lattices), the
determination of the p-neighborhood graph of the Niemeier lattices for
each prime p (the case p=2 being due to Borcherds), or the computation
of the dimension of the space of classical cuspidal Siegel modular
forms for Sp(2g,Z) (with g arbitrary) in weight lessthan or equal to 12.
Joint work with Jean Lannes.

**********************************************************************
P.S. I shall prepare a poster in a week.

[Aloys Krieg]

Dear colleagues,

Please find attached the invitation to our next autormorphic forms
seminar in Lille.

You are cordially invited to participate.

Best regards

Aloys Krieg