**Objective**
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.
Subjects:
● 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
Schedule:
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
**Contact**
Prof. M Manickam
Director, kerala School of Mathematics
e-mail: murugumanick@ksom.res.in
Phone: 0495 2809001
Fax: 0495 2809010 |