# NCMW - Jacobi Forms (2022)

## Speakers and Syllabus

**The following topics are being planned.**

- Preliminary lectures on the theory of modular forms (both integral and half-integral weights)
- Basic properties of Jacobi forms; Eisenstein series; Hecke operators
- Taylor expansion of Jacobi forms; Taylor map
- Relations with other types of modular forms - Half-integral weight; Fourier-Jacobi expansions and Saito-Kurokawa correspondence
- Ring of Jacobi forms - Basic structure theorem; Examples of Jacobi forms of index greater than 1; zeros of Jacobi forms

Names and affiliations |
HRS |
Deatiled Syllabus |

B. Ramakrishnan (ISINEC, Tezpur) (BR1) |
6 hrs | Module 1 : Preliminary lectures on the theory of modular forms (both integral and half-integral weights) |

M. Manickam (IISER, Bhopal) (MM) |
10 hrs | Module 2 : Basic properties of Jacobi forms; Eisenstein series; Hecke operators |

Brundaban Sahu (NISER, Bhubaneswar) (BS) |
8 hrs | Module 3 : Taylor expansion of Jacobi forms; Taylor map |

Karam Deo Shankhadhar (IISER, Bhopal) Jaban Meher (NISER, Bhubaneswar) |
12 hrs | Module 4 :Relations with other types of modular forms - Half-integral weight; Fourier-Jacobi expansions and Saito-Kurokawa correspondence |

Sanoli Gun (IMSc, Chennai) & B. Ramakrishnan (ISINEC, Tezpur) |
12 hrs | Module 5 :Ring of Jacobi forms - Basic structure theorem; Examples of Jacobi forms of index greater than 1; zeros of Jacobi forms |

**Tutors:**

1. (AJ) Dr. Abhash Kumar Jha (IIT BHU);

2. (PT) Mr. Prashant Tiwari (IISER Bhopal).

Each day one lecture of 1.5 hrs and two lectures of 1.25 hrs duration will be there along with one hour tutorial session.

The main reference to this workshop is the following monograph.

M. Eichler, D. Zagier, The theory of Jacobi forms, Progress in Mathematics 55, Birkhauser, 1985.

## Time Table

**Tentative timetable**

Week 1

Day |
Date |
09:45 - 11:15 |
11:45-13:00 |
14:30 - 15:45 |
16:15 - 17:15 |

M | Dec 12 | BR1-1 | BR-12 | MM1 | T1(BR1+AJ) |

T | Dec 13 | MM2 | BR1-3 | BR1-4 | T2(MM+AJ) |

W | Dec 14 | MM3 | BS1 | BS2 | T3(BR1+AJ) |

T | Dec 15 | BS3 | MM4 | BS4 | T4(BS+AJ) |

F | Dec 16 | MM5 | BS5 | MM6 | T5(MM+AJ) |

S | Dec 17 | BS6 | MM7 | BS7 | T6 (BS+AJ) |

**Week 2**

Day |
Date |
09:45 - 11:15 |
11:45-13:00 |
14:30 - 15:45 |
16:15 - 17:15 |

M | Dec 19 | KDS1 | JM1 | KDS2 | T7 (KDS+PT) |

T | Dec 20 | JM2 | KDS3 | JM3 | T8 (JM+PT) |

W | Dec 21 | KDS4 | JM4 | KDS5 | T9 (KDS+PT) |

T | Dec 22 | SG1 | BR2-1 | SG2 | T10 (SG+PT) |

F | Dec 23 | BR2-2 | SG3 | BR2-3 | T11 (BR2+PT) |

S | Dec 24 | SG4 | BR2-4 | SG5 | T12(SG+PT) |

Tea: 11:15- 11:45 & 15:45-16:15; Lunch: 13:00 - 14:30 |