Workshop and International Conference on Automorphic Forms and Number Theory

Kerala School of Mathematics
Kozhikode, Kerala

30 August - 03 September, 2013


Recent developments in various branches of mathematics and physics show an increasing interest in the explicit construction of Jacobi forms, in particular, Jacobi forms of matrix (or, equivalently, lattice) index. This has to do with their appearance in quantum field theory, module spaces of surfaces, infinite dimensional Lie algebras. Though Jacobi forms of matrix index are known since quite long it is only recently that there was an essential breakthrough in the theory. For example, recent work of Gritsenko, Skoruppa, Zagier shows that Jacobi forms can be constructed in a surprisingly explicit way. These constructions in turn are closely related to classical problems in the arithmetic theory of lattices and in the theory of trigonometric polynomials.

For getting interested researchers or graduate students up to date in recent developments we plan to have a 3 days instructional workshop on Jacobi forms of lattice index, followed by a 2 days conference, where participants of the workshop should have an opportunity to report on their own research projects for initiating discussions, obtaining feedback or help.


Part 1: Workshop on Jacobi forms of lattice index
Organizers: Prof. M. Manickam, Prof. Ramakrishnan B., Prof. Nils Peter Skoruppa
Lecturers: Hatice Boylan (Istanbul Üniversitesi and Max-Planck-Institute Bonn), Fabien Cléry (University of Siegen), Nils-Peter Skoruppa (University of Siegen and Max-Planck-Institute Bonn)
Overview: The workshop aims to give a careful and thorough introduction into the theory of Jacobi forms of lattice index with emphasis on explicit constructions, in particular, for low weights and maximal lattices as index. In addition, it will be shown how Jacobi forms can be used to construct other types of automorphic forms via the so-called additive and multiplicative liftings.
● Basic notions: Lattices, shadows, discriminant modules, definition of Jacobi forms, discussion of the definition, first examples, functorial properties
● Jacobi forms as theta functions: vector valued modular forms, relation between Jacobi forms and vector valued modular forms, dimension formulas
● Explicit constructions of Jacobi forms: Taylor expansion around 0, Theta blocks, invariants of Weil representations
● Maximal lattices as index, explicit description of forms of singular and critical weight and maximal index
● Additive and multiplicative liftings, product expansions

Friday to Sunday: each day 3 lectures of 90 min and 60 minutes for discussions, questions and problem session

Part 2: Conference on Automorphic Forms and Number Theory
List of Tentative Speakers

1 Mr. Ali Ajouz Siegen University, Germany
2 Dr. Anandavardhanan .U.K IIT, Mumbai
3 Dr. Bala Subrahmnian IMSc., Chennai
4 Dr. Brundaban Sahu NISER, Bhubaneshwar
5 Dr. Eknath Ghate TIFR, Mumbai
6 Dr. Fabien Cléry France
7 Dr. Hatice Boylan Istanbul University and Max-Planck Institute for Mathematics, Bonn
8 Dr. Jaban Meher IMSc., Chennai
9 Dr. Jagathesan .T RKM vivekananda College, Chennai
10 Dr. Kalyan Chakraborty HRI, Allahabad
11 Dr. Karam Deo Shankhadhar IMSc., Chennai
12 Dr. Kumarasamy .K RKM vivekananda College, Chennai
13 Dr. Manickam .M KSOM, Kozhikode
14 Mr. Mohamed Nishad Faroke College, Kozhikode
15 Dr. Nils Peter Skoruppa Siegen University, Germany
16 Dr. Purusottam Rath CMI, Chennai
17 Mr. Rahothaman .R Sona College of Technology, Salem
18 Dr. Ramakrishnan .B HRI, Allahabad
19 Dr. Ravi Raghunathan IIT, Mumbai
20 Dr. Sanoli Gun IMSc. Chennai
21 Dr. Sengupta .J TIFR, Mumbai
22 Dr. Soumya Das IISc., Bangalore
23 Mr. Srivatsa .V KSOM, Kozhikode
24 Dr. Sujay Ashok IMSc. Chennai
25 Ms. Tamil Selvi Alpha College of Engineering, Chennai

The whole programme is partially suported by HRI, Allahabad


Prof. M Manickam
Director, kerala School of Mathematics
Phone: 0495 2809001
Fax: 0495 2809010