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Apr 4, 2017, 1:42:02 PM4/4/17

to akls-s...@googlegroups.com, Kathrin Bringmann, Jan Hendrik Bruinier, Aloys Krieg, mo...@mpim-bonn.mpg.de, Nebe, Sander Zwegers, Emmanuel Royer, Gaetan Chenevier, Evgeny Ferapontov

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.

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.

Apr 8, 2017, 5:35:32 AM4/8/17

to akls-s...@googlegroups.com, assis...@matha.rwth-aachen.de, s718....@gmail.com, Sho Takemori

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

Please find attached the invitation to our next autormorphic forms

seminar in Lille.

You are cordially invited to participate.

Best regards

Aloys Krieg

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