Automorphic forms, Kac-Moody Lie algebras and Strings

Explicit constructions in the theory of automorphic forms and applications

During the past decade automorphic forms have been successfully used to solve some fundamental problems in algebraic geometry and the theory of Kac--Moody algebras. Special Siegel modular forms and mock theta-series have become an important tool in the theory of supergravity.

The main research aims of the program are:

1. To study reflective modular forms and the corresponding reflective hyperbolic lattices of different ranks and the corresponding Kac--Moody Lie algebras of Borcherds type;
2. To classify the so-called theta-blocks, the special Jacobi modular forms with infinite product structure, which are intermediate objects between Borcherds automorphic products and the usual SL(2)-modular forms.  To consider the corresponding vector-valued modular forms and Weil representations. To study Siegel modular forms of genus two of small weights, specially of weights 2 and 3.
3. To study the birational type of different moduli spaces using special automorphic forms with large divisors. More explicitly, to determine the birational type of the moduli spaces of lattice polarised K3 surfaces and the moduli spaces of polarised irreducible symplectic varieties, including the special symplectic O'Grady varieties of dimension 10.

Workshop related to this MPI program:

"Automorphic forms, Kac-Moody Lie algebras and Strings."

May 10--14, 2010.

Recent progress in string theory and the theory of supergravity shows that the generating functions for the quantum degeneracies of supersymmetric black holes are related to reflective Siegel modular forms and mock theta-series. Reflective Siegel forms determine Kac-Moody Lie algebras of Borcherds type which are also important in physics.  The main idea of this workshop is to present the current results in this field related to string theory, the theory of automorphic forms and the theory of Kac-Moody Lie algebras.



Participants:

A. Andrianov (St.Petersburg) May--June
D. Allcock (Austin, USA)     May 16 --June 26
F. Clery (Amsterdam)         April--May
V. Gritsenko (Lille)         January--June
K. Hulek (Hannover)          March
T. Ibukiyama (Osaka)         May (?)
K. Iohara (Lyon)             June
V. Nikulin (Liverpool)       March 26-- April 25
C. Poor (USA)                March 12 to March 21,
G. Sankaran (Bath)           February 21--March 14
N.-P. Skoruppa (Siegen)      April-May
K.-I. Yoshikawa (Kyoto)      May (?)
D. Yuen (USA)                March 12 to March 21