Conference on Jacobi Forms and Applications

Centre International des Rencontres Mathématiques in Luminy (near Marseille, France)
September 24-28, 2001.
Organization: Valery Gritsenko and Nils-Peter Skoruppa

The last years have shown an increasing interest in Jacobi forms: in fact, there are applications in arithmetic and algebraic geometry, in the theory of Kac-Moody and vertex operator algebras and in theoretical physics, not to mention applications to lattice and coding theory.

As examples one may cite articles of Freitag, Gritsenko and Hulek on the geometry of moduli spaces of abelian varieties, articles of Borcherds on moduli spaces of Enrique surfaces and cubic surfaces, on automorphic products, and the succeeding articles of Freitag, Gritsenko et Nikulin, finally the of articles of Dijkgraaf, Moore et Kawai on the second quantized elliptic genus. There is also recent progress in the proper theory of Jacobi forms, e.g. work of Guerzhoy on p-adic properties of Jacobi forms and some recent ideas of Ibukiyama and Skoruppa to exploit skew-holomorphic Jacobi forms for the study of non-holomorphic Siegel modular forms,

The conference wants to give an account of the actual status quo of the theory of Jacobi forms and its applications, and to indicate recent trends or even new perspectives.




Some useful links     






Program for Monday, September 24

8h55Opening
9h - 9h50 R.Berndt Applications of Jacobi theory in Physics
10h10 - 11h T. Gannon The character of a vertex operator algebra
11h10 - 12h T. Ibukiyama Siegel modular forms of half integral weights and a lifting conjecture
12h30Lunch
16h - 16h50 G.K. Sankaran Moduli of abelian surfaces with bilevel structure
17h - 17h50 S. Böcherer Modular forms with high vanishing order
18h10 - 19h S. Zwegers Fourier Coefficients of Meromorphic Jacobi Forms
19h30Dinner





Program for Tuesday, September 25

9h - 9h50 R. Schmidt Representation theoretic aspects of Jacobi forms
10h10 - 11h X. Wang Shimura liftings and a congruence relation between Eisenstein series
11h10 - 12h H. Aoki Jacobi forms, Fourier Jacobi developments and the ring structure of automorphic forms
12h30Lunch
16h - 16h50 V. Nikulin Reflection groups in hyperbolic spaces and Jacobi forms
17h - 17h50 F. Smirnov On affine Jacobians of spectral curves
19h30Dinner





Program for Wednesday, September 26

9h - 9h50 K. Hulek The modularity of certain Calabi-Yau varieties
10h10 - 11h T. Arakawa Selberg zeta functions and dimension formulas
11h10 - 12h A. Pantchichkine Families of p-adic nearly holomorphic functions
12h30Lunch
14h Excursion
19h30Dinner





Program for Thursday, September 27

9h - 9h50 C. Bachoc Lattices, designs and differential operators on Siegel modular forms (joint work with G. Nebe)
10h10 - 11h E. Bannai Fractional weight modular forms
11h10 - 12h P. Sole Ozeki polynomials
12h30Lunch
16h - 16h50 W. Kohnen Zeros and Poles of modular forms and Jacobi forms
17h - 17h50 R. Salvati Manni Modular varieties, Thetanullwerte and Riemann's relations
18h10 - 19h H. Skogman Jacobi forms and vector-valued modular forms
19h30Special Dinner





Program for Friday, September 28

9h - 9h50 V. Maillot Moduli of abelian varieties with endomorphism structures and Gross-Deligne conjecture
10h10 - 11h I. Galvez Jacobi forms, formal group laws and manifolds with boundary
11h10 - 12h B. Ramakrishnan On a correspondence between Jacobi forms and modular forms
12h30Lunch
16h - 16h50 I. Potemin Higher-dimensional Langlands duality, S-duality and Jacobi forms
17h10 - 18h00 M. Manickam On Jacobi Eisenstein series
19h30Dinner





Final List of Invited Participants and Talks

Name Preliminary Title of Talk Institute Email Home Page
Aoki, Hiroki Jacobi forms, Fourier-Jacobi developments and the ring structure of automorphic forms Ritsumeikan Univ., Japan
Arakawa, Tsuneo Selberg zeta functions and dimension formulas Rikkyo Univ., Japan
Bachoc, Christine Lattices, designs and differential operators on Siegel modular forms (joint work with G. Nebe) Bordeaux, France
Bannai, Eiichi Fractional weight modular forms Kyushu, Japan
Berndt, Rolf Applications of Jacobi theory in Physics Hamburg, Germany
Boecherer, Siegfried Modular forms with high vanishing order Mannheim, Germany
Bhowmik, Gautami Lille, France
Desreumaux, Caroline Lille, France
El Gradechi, Amine Lens, Fr
Galvez, Imma Jacobi forms,formal group laws and manifolds with boundary Sheffield, UK
Gannon, Terry The character of a vertex operator algebra Alberta, CA
Gritsenko, Valery Lille, France
Hulek, Klaus The modularity of certain Calabi-Yau varieties Hannover, Germany
Ibukiyama, Tomoyoshi Siegel modular forms of half integral weights and a lifting conjecture Osaka, Japan
Kohnen, Winfried Zeros and Poles of modular forms and Jacobi forms Heidelberg, Germany
Maillot, Vincent Moduli of abelian varieties with endomorphism structures and Gross-Deligne conjecture Jussieu, Fr
Manickam, Murugesan to be announced Mylapore, India
Manni, Riccardo Salvati Modular varieties, Thetanullwerte and Riemann's relations U. La Sapienza, Rome, Italy
Nebe, Gabriele Ulm, Germany
Nikulin, Viacheslav V. Reflection groups in hyperbolic spaces andJacobi forms Liverpool, UK
Pantchichkine, Alexei Families of p-adic nearly holomorphic functions Grenoble, France
Potemine, Igor Higher-dimensional Langlands duality, S-duality and Jacobi forms Toulouse, France
Ramakrishnan, B. On a correspondence between Jacobi forms and modular forms Harish-Chandra RI, Allahabad, India
Sankaran, G.K. Moduli of abelian surfaces with bilevel structure Bath, England
Schmidt, Ralf Representation theoretic aspects of Jacobi forms Saarbrücken, Germany
Schulze-Pillot, Rainer Saarbrücken, Germany
Skogman, Howard Jacobi forms and vector-valued modular forms SUNY Brockport, USA
Skoruppa, Nils-Peter Siegen, Germany
Smirnov, Fedor. On Affine Jacobians of Spectral Curves Jussieu, Fr
Solé, Patrick Ozeki polynomials Nice, France
Wang, Xueli Shimura liftings and a congruence relation between Eisenstein series Essen, Ger. and China
Zwegers, Sander Fourier Coefficients of Meromorphic Jacobi Forms (and Mock Theta Functions) Utrecht, NL.

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