Jacobi Forms (2022)

Convener(s)

 
Name: B. Ramakrishnan Rupam Barman
Mailing Address: Indian Statistical Institute North-East Centre
Punioni, Solmara
Tezpur 784 501		 Department of Mathematics
Indian Institute of Technology Guwahati
North Guwahati
Guwahati 781 039
Email: b.ramki61 at gmail.com rupambarman at gmail.com

Jacobi forms arise naturally as the Fourier coefficients (Fourier-Jacobi exapnsion) of Siegel modular forms. A systematic study of these automorphic forms was studied by Martin Eichler and Don Zagier in the monographpublished in 1985. Jacobi forms play an important role in proving the famous Saito-Kurokawa conjecture, which gives a connection between Siegel modular forms of degree 2 and elliptic modular forms. There is also a connection between Jacobi forms and modular forms of half-integral weight.Due to connections with various types of automorphic forms, the theory of Jacobi forms play a key role in the theory of automorphic forms.

In order to motivate young researchers, we propose to organise a two weeks NCM workshop on Jacobi forms. In this workshop, we mainly cover the important topics discussed in the above mentioned monograph (Progressin Mathematics vol. 55), which is the main source of reference for this workshop. Since basic knowledge of the theory of modular forms of both integral and half-integral weights are needed, we also plan to cover some preliminary materials on the theory of modular forms in the beginning.

Dates: 

Monday, December 12, 2022 - 11:15 to Saturday, December 24, 2022 - 11:15

Venue: 

Venue Address: 

Indian Statistical Institute, North-East Centre, Tezpur
and Indian Institute of Technology, Guwahati.

Venue State: 

Venue City: 

PIN: 

781039

Chrono Order: 

403

Syllabus: 

The following topics are being planned.

  1. Preliminary lectures on the theory of modular forms (both integral and half-integral weights)
  2. Basic properties of Jacobi forms; Eisenstein series; Hecke operators
  3. Taylor expansion of Jacobi forms; Taylor map
  4. Relations with other types of modular forms - Half-integral weight; Fourier-Jacobi expansions and Saito-Kurokawa correspondence
  5. 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)
(BR2)

 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

 

 

 

Selected Applicants: 

 

The selected candidates should confirm their participation by 30th Sept 2022 (by sending an email to both the organisers)
b.ramki61@gmail.com, rupambarman@gmail.com
 
Serial SID Full Name Gender Affiliation Position in College/ University University/ Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Degree Date
  Local participants    
1 43154 Dr. Jaitra Chattopadhyay Male IIT Guwahati Post-Doctoral Fellow Ramakrishna Mission Vidyamandira 2015 16/06/2020
2 42778 Mr Shaik Azharuddin Male IIIT Guwahati PhD University of Mysore 2019  
3 43017 Mr. Ajit Singh Male Indian Institute of Technology Guwahati Research Associate Indian Institute of Technology Guwahati 2017 17/06/2022
4 43022 Mr. Gurinder Singh Male Indian Institute of Technology Guwahati PhD Panjab University, Chandigarh 2019  
5 43029 Ms. Sulakashna - Female INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI Research Scholar Indian Institute of Technology Guwahati 2020  
6 43140 Ms H Laxmi Female Indian Institute of Technology Guwahati PhD Student Indian Institue of Technology Guwahati 2020  
  Outstation Participants      
1 41512 Dr Mohit Tripathi Male National Institute of Science Education and Research (NISER) Research Associate Indian Institute of Technology Guwahati, Assam 2015 19/01/2021
2 41671 Dr. Anup Kumar Singh Male National Institute of Science Education and Research (NISER) Bhubaneshwar Postdoc BHU Varanasi 2012 26/07/2019
3 41754 Mr. Shubham Shravan Jaiswal Male Indian Institute of Science Education and Research Pune (IISER Pune) IntPhD Mathematics IISER Pune Int PhD Mathematics 2020  
4 41774 Mr Nilanjan Bag Male Ramakrishna Mission Vivekananda Educational and Research Institute Postdoc Ramakrishna Mission Vidyamandira, Belur Math 2015 21/12/2020
5 41875 Mr. Sunil L Naik Male The Institute of Mathematical Sciences   University of Hyderabad, Telangana    
6 41886 Ms. Rashi Sanjay Lunia Female The Institute of Mathematical Sciences PhD student Sardar Patel University (M.Sc.) 2019  
7 41887 Mr. Animesh Sarkar Male Indian Institute of Technology (BHU) Varanasi PhD Student University of North Bengal 2018  
8 41935 Mr. Shivajee . Male IIT Gandhinagar PhD Scholar M.Sc. 2017  
9 42112 Mr. Shivansh Pandey Male National Institute of Science Education and Research, Bhubaneswar PhD Banaras Hindu University, Varanasi 2019  
10 42329 Ms. Meghali Garg Female IIT Indore PhD IIT Gandhinagar 2019  
11 42335 Mr Mohd Harun Male IIT Kanpur PhD M.Sc. Mathematics 2018 01/01/2019
12 42342 Mr. Vaibhav Kalia Male Indian Institute of Technology Ropar PhD student Motilal Nehru National Institute of Technology, Allahabad 2018  
13 42346 Dr. Lalit Vaishya Male School of Mathematical Sciences
National Institute of Science Education and Research Bhubaneswar		 Post Doctoral Fellow BANARAS HINDU UNIVERSITY VARANASI 2014 13/08/2021
14 42637 Mr Mrityunjoy Charan Male National Institute of Science Education and Research PhD Indian Institute of Technology Guwahati 2018  
15 42643 Mr. Prabhat Kumar Mishra Male INDIAN INSTITUTE OF TECHNOLOGY JAMMU PhD Student Indian Institute of Technology Guwahati 2021  
16 42770 Dr. Sandeep E M Male ISI North East Centre Research Associate (Post Doc) IISER Thiruvananthapuram 2015 14/02/2022
17 42901 Mr Vishakh Vasu Male Indian Institute of Science Education and Research. MS IISER Bhopal,BS-MS Appeared / Awaiting Result  
18 42944 Mr Sumukha S Male IIT Gandhinagar Postdoctoral fellow Mangalore University 2017  
19 42950 Mr Sreejith M M Male Kerala School of Mathematics PhD Student IISER Thiruvananthapuram 2016  
20 42976 Mr. Adersh V K Male TKM College of Arts and Science (Part time research scholar, KSoM) Assistact Professor University of Kerala 2005  
21 43008 Dr. Manish Kumar Pandey Male SRM AP Asst. Prof ISI, Bangalore 2011  
22 43014 Dr. Saurabh Kumar Singh Male IIT Kanpur Assistant professor     09/09/2015
23 43040 Dr. Rishabh Agnihotri Male Indian Institute of Science, Bengaluru Post-doc Fellow IIT Kanpur, Kanpur 2017 08/03/2022
24 43059 Ms. Shivani Goel Female Indraprastha Institute of Information Technology Delhi PhD Chaudhary Charan Singh University, Meerut 2018  
25 43088 Ms Priyanka Majumder Female IISER Pune Research Associate IIT Hyderabad 2016 17/12/2021
26 43117 Mr. Subhrajyoti Bhattacharyya Male NIT Agartala PhD Student IIT Guwahati 2019  
27 43155 Mr. Shamik Das Male Harish-Chandra Research Institute Post Doctoral Fellow IIT Guwahati 2016 24/09/2021
28 43163 Mr. Arunabha Mukhopadhyay Male The Institute of Mathematical Sciences, Chennai PhD Indian Institute of Technology Kanpur 2019  
29 43165 Mr Sagar Shrivastava Male Tata Institute of Fundamental Research PhD NISER, Bhubaneshwar 2016  
30 43169 Mr. Pranjal Vishwakarma Male IISER PUNE Integrated PhD IISER PUNE 2019  
  Wait-listed participants      
1 43036 Mr. Pranjal Talukdar Male Tezpur University PhD Student Tezpur University 2020  
2 41859 Dr. Karthick Babu C G Male IISER-Berhampur Post doctoral fellow Madurai Kamaraj University 2014 23/12/2021
3 41888 Mr Mohd Shahvez Alam Male IIT BHU PhD Student IIT Hyderabad 2019  
4 42328 Mr Archit Agarwal Male IIT Indore PhD IIT Gandhinagar 2018  
5 42790 Ms. Himanshi Chanana Female IIT Kanpur PhD IIT Ropar 2019  
6 43049 Mr. Sushant Kala Male The Institute of Mathematical Sciences PhD I I T Ropar 2020  
7 43054 Mr. Darshan Prafulbhai Nasit Male Indian Institute of Science Education and Research Pune PhD Student IISER Pune 2019  
8 43074 Mr. Bittu . Male Indraprastha Institute of Information Technology Delhi (IIIT-D) PhD Indian Institute of Technology Roorkee 2019  
9 43093 Mr. Bhishek Garg Male Indian Statistical Institute, Bangalore Centre MSc Student Indian Statistical Institute Bangalore Centre    
10 43142 Dr. Subramani Muthukrishnan Male Indian Institute of Information Technology, Chennai Asst. Prof. University of Madras 2009 08/01/2018

 

Accommodation: New Guest House, IIT Guwahati
Check-in date: 11th December 2022
Check-out date: 25th December 2022

 

How to Reach: 

Click here

School Short Name: 

jf

Last Date Application: 

Friday, November 5, 2021

School Type: 

NCMW

Separate faculty form: 

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