Jacobi Forms (2022)

Venue: IIT,  Guwahati, Assam
Date:  12th, Dec 2022 to 24th, Dec 2022

 

School Convener(s)
Name B. Ramakrishnan Rupam Barman
Mailing Address Indian Statistical Institute North-East Centre
Punioni, Solmara
Tezpur 784 501
Assam		 Department of Mathematics
IIT Guwahati
North Guwahati,
Assam-781039

 

List of the actual speakers:

Sl. No. Name of the speaker Position Affiliation
1. B. Ramakrishnan Professor & Head Indian Statistical Institute North-East Centre, Tezpur
2. M. Manickam Adjunct Professor IISER Bhopal
3. Brundaban Sahu Associate Professor NISER Bhubaneswar
4 Jaban Meher Associate Professor NISER Bhubaneswar
5 Karam Deo Shankhadhar Associate Professor IISER Bhopal
6 Abhash Jha Associate Professor IIT (BHU) Varanasi

 List of the actual tutors:

Sl. No. Name of the tutor Position Affiliation
1. Abhash Jha Assistant Professor IIT (BHU) Varanasi
2. Prashant Tiwari Post-doctoral fellow HRI Prayagraj

 

 Syllabus:  

Actual syllabus covered by each speaker:

Sl. No.  Name of the Speaker Detailed Syllabus
1 B. Ramakrishnan Introduction to the theory of modular forms of integral weight; examples, Hecke operators, Ramanujan’s conjectures, forms of higher level, Atkin-Lehner theory of newforms; Introduction to the theory of modular forms of half-integral weight, examples, Hecke operators, Shimura correspondence.Theory of new forms of half-integral weight (brief description of a paper of W. Kohnen).
2 M. Manickam Definition of modular forms of integral weight, Fourier expansion of Eisenstein series, Jacobi group; Definition of Jacobi forms, Jacobi Eisenstein series and Fourier expansion; Finite dimensionality of Jacobi space, Petersson scalar product, Poincare series; Operators on Jacobi forms - preparatory results; Hecke operators on Jacobi forms and Fourier expansion; Fourier expansion of operators, related results; Theta functions and lattices, Quadratic forms, Siegel modular forms – connections; Theory of newforms for Jacobi forms and its link with half-integral weight forms via Eichler-Zagier map; Generalisation of the Eichler-Zagier map for higher index and level.
3 Brundaban Sahu Structure of Jacobi forms of even weight of a fixed index as a module over the ring of modular forms; Structure of Jacobi forms of even weight of index two as a module over the ring of modular forms (finding three free generators); Structure of Jacobi forms  as a module over the ring of  modular forms; Structure of the ring of Jacobi forms;  Explicit dimension formula of the vector space of Jacobi form of a given weight and index through study of filtration and weak Jacobi forms; Structure of the ring of weak Jacobi forms of even weight as  a polynomial algebra over the ring of modular forms; Structure of the ring of weak Jacobi forms.
4 Jaban Meher Taylor expansions of Jacobi forms, Differential operators on Jacobi forms, Rankin-Cohen brackets of Jacobi forms; Basics of Siegel modular forms, Fourier-Jacobi expansions of Siegel modular forms, Spinor zeta function, Saito-Kurokawa conjecture, characterization of Saito-Kurokawa lift.
5 Karam Deo Shankhadhar The theta decomposition of Jacobi forms, Understanding the properties of the theta components of Jacobi forms, Relation between the Petersson inner product of two Jacobi cusp forms in terms of the inner product of its theta components, Eichler-Zagier isomorphism between Jacobi forms of index 1 and the half-integral weight plus space of level 4, Eichler-Zagier map from Jacobi forms of arbitrary index into the half-integral modular forms, Certain correspondence between the spaces of Jacobi forms and integral weight modular forms, certain relation among the Fourier coefficients of Jacobi forms and central L-values of certain integral weight modular forms.
6 Abhash Jha Applications of Taylor map: Estimate for the dimension of the space of Jacobi forms of weight k and index m; the dimension of the space of Jacobi forms and Jacobi cusp forms of weight k and index one; Commutativity of the Taylor map and the Hecke operator V_l, relation between Taylor map and the Rankin-Cohen bracket, Jacobi-Poincare series and properties; Adjoint of the product map on the space of cusp forms (Kohnen’s work); Image of Jacobi-Poincare series under the Taylor map, and the adjoint of Taylor map, Satoh’s map.

 

 Time Table

Actual time-table that was followed during the programme:

Week 1

Day

Date

9:30-11:00

 

11:30-12:45

14:30-15:45

 

16:15-17:15

 

MON

12/12/22

BR1

T

BR2

MM1

T

T1 (BR+AJ)

S

TUE

13/12/22

MM2

 

BR3

BR4

 

T2 (MM+AJ)

N

WED

14/12/22

MM3

E

JM1

JM2

E

T3 (BR+AJ)

A

THU

15/12/22

JM3

 

MM4

AJ1

 

T4 (JM+AJ)

C

FRI

16/12/22

MM5

A

AJ2

MM6

A

T5 (MM+AJ)

K

SAT

17/12/22

AJ3

 

MM7

AJ4

 

T6 (JM+AJ)

S

 

Week 2

Day

Date

9:30-11:00

 

11:30-12:45

14:30-15:45

 

16:15-17:15

 

MON

19/12/22

KDS1

T

JM4

KDS2

T

T7 (KDS+PT)

S

TUE

20/12/22

JM5

 

KDS3

JM6

 

T8 (JM+PT)

N

WED

21/12/22

BS1

E

KDS4

BS2

E

T9 (KDS+PT)

A

THU

22/12/22

JM7

 

KDS5

BS3

 

T10 (BS+PT)

C

FRI

23/12/22

BS4

A

JM8

BR5

A

T11 (JM+PT)

K

SAT

24/12/22

MM8

 

KDS6

MM9

 

T12 (BS+PT)

S

 

Full forms for the abbreviations of speakers and tutors:

BR: B. Ramakrishnan
MM: M. Manickam
JM: Jaban Meher
AJ: Abhash Jha
KDS: Karam Deo Shankhadhar
BS: Brundaban Sahu
PT: Prashant Tiwari

List of actual Participants

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
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  
7 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
8 41671 Dr. Anup Kumar Singh Male National Institute of Science Education and Research (NISER) Bhubaneshwar Postdoc BHU Varanasi 2012 26/07/2019
9 41754 Mr. Shubham Shravan Jaiswal Male Indian Institute of Science Education and Research Pune (IISER Pune) IntPhD Mathematics IISER Pune Int PhD Mathematics 2020  
10 41774 Mr Nilanjan Bag Male Ramakrishna Mission Vivekananda Educational and Research Institute Postdoc Ramakrishna Mission Vidyamandira, Belur Math 2015 21/12/2020
11 41875 Mr. Sunil L Naik Male The Institute of Mathematical Sciences   University of Hyderabad, Telangana    
12 41886 Ms. Rashi Sanjay Lunia Female The Institute of Mathematical Sciences PhD student Sardar Patel University (M.Sc.) 2019  
13 41887 Mr. Animesh Sarkar Male Indian Institute of Technology (BHU) Varanasi PhD Student University of North Bengal 2018  
14 41935 Mr. Shivajee . Male IIT Gandhinagar PhD Scholar M.Sc. 2017  
15 42112 Mr. Shivansh Pandey Male National Institute of Science Education and Research, Bhubaneswar PhD Banaras Hindu University, Varanasi 2019  
16 42329 Ms. Meghali Garg Female IIT Indore PhD IIT Gandhinagar 2019  
17 42342 Mr. Vaibhav Kalia Male Indian Institute of Technology Ropar PhD student Motilal Nehru National Institute of Technology, Allahabad 2018  
18 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
19 42637 Mr Mrityunjoy Charan Male National Institute of Science Education and Research PhD Indian Institute of Technology Guwahati 2018  
20 42643 Mr. Prabhat Kumar Mishra Male INDIAN INSTITUTE OF TECHNOLOGY JAMMU PhD Student Indian Institute of Technology Guwahati 2021  
21 42770 Dr. Sandeep E M Male ISI North East Centre Research Associate (Post Doc) IISER Thiruvananthapuram 2015 14/02/2022
22 42901 Mr Vishakh Vasu Male Indian Institute of Science Education and Research. MS IISER Bhopal,BS-MS Appeared / Awaiting Result  
23 42944 Mr Sumukha S Male IIT Gandhinagar Postdoctoral fellow Mangalore University 2017  
24 42950 Mr Sreejith M M Male Kerala School of Mathematics PhD Student IISER Thiruvananthapuram 2016  
25 42976 Mr. Adersh V K Male TKM College of Arts and Science (Part time research scholar, KSoM) Assistact Professor University of Kerala 2005  
26 43040 Dr. Rishabh Agnihotri Male Indian Institute of Science, Bengaluru Post-doc Fellow IIT Kanpur, Kanpur 2017 08/03/2022
27 43088 Ms Priyanka Majumder Female IISER Pune Research Associate IIT Hyderabad 2016 17/12/2021
28 43117 Mr. Subhrajyoti Bhattacharyya Male NIT Agartala PhD Student IIT Guwahati 2019  
29 43155 Mr. Shamik Das Male Harish-Chandra Research Institute Post Doctoral Fellow IIT Guwahati 2016 24/09/2021
30 43163 Mr. Arunabha Mukhopadhyay Male The Institute of Mathematical Sciences, Chennai PhD Indian Institute of Technology Kanpur 2019  
31 43165 Mr Sagar Shrivastava Male Tata Institute of Fundamental Research PhD NISER, Bhubaneshwar 2016  
32 43169 Mr. Pranjal Vishwakarma Male IISER PUNE Integrated PhD IISER PUNE 2019  
33   Maibam Ricky Devi   PhD student   Gauhati University    
34   Dr. Mohit Mishra   Post-doc   Indian Institute of Technology (IIT) Guwahati    

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