AIS Modular Forms (2019)

Venue: IIT Guwahati,  Guwahati, Assam
Date:  13th, May 2019 to 1st, Jun 2019

 

School Convener(s)
Name Prof. Anupam Saikia Dr. Rupam Barman
Mailing Address

Dept. of Mathematics,
Indian Institute of Technology Guwahati,
Guwahati 781039

Dept. of Mathematics,
Indian Institute of Technology Guwahati,
Guwahati 781039

 

 Speakers with their affiliations:

Name of the speaker

Affiliation

Prof.Anupam Saikia IIT Guwahati
Dr.Rupam Barman IIT Guwahati
Dr.Soumya Das IISc Bangalore
Dr.Debargha Banerjee IISER Pune
Dr.Narasimha Kumar IIT Hyderabad
Prof. B. Ramakrishnan HRI, Allahabad

 List of Tutors

Name of the tutor

Affiliation
Nilanjan Bag

IIT Guwahati

Pramath Anamby

IISc Bangalore

Manish Kumar Pandey

HRI, Allahabad

 

 Syllabus:

Name of the Speaker

Detailed Syllabus
Prof.Anupam Saikia
IIT Guwahati
Six lectures

  1. The full modular group

  2. Congruence subgroups

  3. Action on the upper half plane, elliptic points, cusps

  4. Fundamental domain, compactification, volume

Dr.Rupam Barman
IIT Guwahati
Eight lectures

  1.  Fourier expansion

  2.  Eisenstein series

  3.  Dimension formulae, zeros and poles using contour integrals, valence formula

  4.  Hecke operators

  5.  Ramanujan’s tau function, j-function and  its relevance

Dr.Soumya Das,
IISc Bangalore
Six lectures

  1. Modular forms for congruence subgroups

  2. Eisenstein series of higher level for $Gamma_0(N),\Gamma_1(N)$

  3. Peterson inner product
Dr.Debargha Banerjee,
IISER Pune
Six lectures

  1. Double coset operators

  2. Oldforms and newforms, Atkin-Lehner Theory

  3. Heckeeigneform
Dr.Narasimha Kumar,
IIT Hyderabad
Five lectures

  1. Halh integral weight modular forms: Definition and examples Non-vanishing of Fourier coefficients

  2. number theoretic applications

  3. Shimura Correspondence

  4. Hecke Theory for half-integral weight forms

  5. Fourier coefficients and it’s relation with L-values of the associated Shimura lift
Prof. B. Ramakrishnan,
Harish-Chandra Research Institute, Allahabad
Five lectures

  1. Euler product

  2. Functional equation, relation between elliptic curves and modular forms

  3. Converse Theorems of Hecke

 

 Time Table

Day

Date

Lecture 1

(09.30-11.00)

Tea

 

Lecture 2

(11.30-01.00)

Lunch

 

Tutorial

(02.30-3.30)

Tea

Tutorial

(4-5)

Snacks

MON

13.05.2019

AS-1

 

RB-1

L

(AS, NB)

 

(AS, NB)

S

TUE

14.05.2019

AS-2

T

RB-2

U

(RB, NB)

T

(RB, NB)

N

WED

15.05.2019

RB-3

E

AS-3

N

(AS, NB)

E

(AS, NB)

A

THU

16.05.2019

RB-4

A

AS-4

C

(RB, NB)

A

(RB, NB)

C

FRI

17.05.2019

AS-5

 

RB-5

H

(AS, NB)

 

(AS, NB)

K

SAT

18.05.2019

AS-6

 

RB-6

 

(RB, NB)

 

(RB, NB)

S

 

MON

20.05.2019

SD-1

 

RB-7

L

(SD, PA)

 

(SD, PA)

S

TUE

21.05.2019

SD-2

T

RB-8

U

(RB, NB)

T

(RB, NB)

N

WED

22.05.2019

DB-1

E

SD-3

N

(SD, PA)

E

(SD, PA)

A

THU

23.05.2019

SD-4

A

DB-2

C

(DB, PA)

A

(DB, PA)

C

FRI

24.05.2019

DB-3

 

SD-5

H

(SD, PA)

 

(SD, PA)

K

SAT

25.05.2019

SD-6

 

DB-4

 

(DB, PA)

 

(DB, PA)

S

 

MON

27.05.2019

BR-1

 

DB-5

L

(DB, MKP)

 

(DB, MKP)

S

TUE

28.05.2019

NK-1

T

DB-6

U

(NK, MKP)

T

(NK, MKP)

N

WED

29.05.2019

BR-2

E

NK-2

N

(BR, MKP)

E

(BR, MKP)

A

THU

30.05.2019

BR-3

A

NK-3

C

(NK, MKP)

A

(NK, MKP)

C

FRI

31.05.2019

BR-4

 

NK-4

H

(BR, MKP)

 

(BR, MKP)

K

SAT

1.06.2019

BR-5

 

NK-5

 

(NK, MKP)

 

(NK, MKP)

S

AS: Anupam Saikia (IITG), RB: Rupam Barman (IITG), SD: Soumya Das (IISc Bangalore),

DB: Debargha Banerjee (IISER Pune), NK: Narasimha Kumar (IIT Hyderabad)

BR: B. Ramakrishnan (HRI Allahabad)

NB: Nilanjan Bag (IITG), PA: Pramath Anamby (IIScBangalore)

MKP: Manish Kumar Pandey (HRI Allahabad)

List of actual Participants

Sr SID Full Name Gender Affiliation Position in College/ University University/ Institute M.Sc./M.A. Year of Passing M.Sc./ M.A Ph.D. Deg
Date
1 24504 Mr Sunil Kumar Pasupulati Male IISER TVM PhD student IISER TVM 2018  
2 24509 Mr. Anup Das Male Gauhati University PhD Gauhati University 2017  
3 24536 Mr. Shomavo Chakraborty Male Assam Don Bosco University PhD Assam University 2010  
4 24548 Mr Lalit Vaishya Male HCRI Prayagraj (Allahabad) Research Scholar BHU Varanasi 2014  
5 24552 Mr. Mohit Mishra Male HCRI Ph.D. IIT MADRAS 2017  
6 24576 Mr. Krishnarjun K Male HCRI PhD Central University of Tamil Nadu 2018  
7 24603 Mr. Subhajit Bandyopadhyay Male Tezpur University PhD Student Tezpur University 2017  
8 24666 Mr. Satyabrat Sahoo Male IIT, Hyderabad Ph.D. Pondicherry University 2016  
9 24677 Mr. Hirakjyoti Das Male Tezpur University, Napaam, India PhD Student Tezpur University, Tezpur 2017  
10 24810 Dr. Bibekananda Maji Male IITGandhinagar Post Doctoral Fellow IIT Bombay 2010 24/04/2017
11 24815 Ms Srijonee Shabnam Chaudhury Female Harish-chandra Research Institute Phd Student jadavpur university 2015  
12 24824 Mr. Rishabh Sarma Male International Centre for Theoretical Sciences, Bangalore Long term visiting student Indian Institute of Technology, Guwahati, M.Sc. 2018  
13 24829 Ms Srimathi Varadharajan Female University of Bergen PhD Student University of London 2015  
14 25000 Mr. Rishabh Agnihotri Male HCRI Phd IIT Kanpur 2017  
15 25028 Ms. Anwita Bhowmik Female IIT Guwahati Ph.D Jadavpur University 2017  
16 25035 Mr Sohan Ghosh Male Sohan Ghosh PhD Indian Institute of Technology, Guahati 2017  
17 25118 Ms. Sehra Sahu Female National Institute of Technology Karnataka, Surathkal PhD Student Central University of Karnataka 2016  
18 25169 Mr. Suneel Kumar Male IISER Mohali PhD Student IIT Kanpur 2017  
19 25428 Mr. Abdul Hannan Male Indian Statistical Institute MSc Student Indian Statistical Institute    
20 25444 Mr. Abinash Sarma Male IISER TVM Integrated PhD IISER TVM 2017  
21 25500 Mr. Rahul Kumar Male IIT Gandhinagar PhD student IIT Kanpur; M.Sc 2015  
22 25556 Mr. Rajat Gupta Male IIT Gandhinagar PhD Student IIT Kanpur 2015  
23 26018 Mr. Adersh V K Male Kerala School of Mathematics Research Scholar (Part-time) University of Kerala 2005  
24 26074 Dr. Anuj Jakhar Male The Institute of Mathematical Sciences, Chennai Post-doctoral fellow Indian Institute of Science Education and Research Mohali 2014 25/05/2018
25 26100 Mr. Sandeep E M Male Kerala School of Mathematics Senior Research Fellow IISER Trivandrum 2015  
26 26108 Ms Pratiksha Satish Shingavekar Female IIT Madras Research Scholar University of Pune 2017  
27 26113 Mr Nilanjan Bag Male IIT Guwahati PhD Ramakrishna Mission Vidyamandira 2015  
28 26128 Mr Sreejith M M Male Kerala School of Mathematics PhD student IISER Thiruvananthapuram 2016  
29 26162 Mr Dilip Kumar Sahoo Male IISER , BERHAMPUR PhD student M.Sc Utkal University , Bhubaneswar , Odisha 2015  
30 26172 Mr. Aritram Dhar Male IISER Mohali BS-MS Student IISER Mohali Appeared  
31 26272 Mr. Ajit Singh Male Indian Institute of Technology PhD IIT Guwahati 2017  
32 26292 Mr Mohit Tripathi Male IIT Guwahati Phd IIT Guwahati 2015  
33 26347 Mr. Shubham Gupta Male HCRI Ph.d IIT Kanpur 2018  
34 26420 Mr Pronay Kumar Karmakar Male IISER Mohali PhD Tezpur University 2017  
35 26565 Mr Sumukha S Male NITK, Surathkal PhD Student Mangalore University` 2017  
36 26622 Dr. Ranganatha Dasappa Male Central University of Karnataka Assistant Professor University of Mysore 2012 19/10/2017
37 26747 Ms. Swati . Female The Institute of Mathematical Sciences (IMSc Chennai) Visiting Researcher Thapar Institute of Engineering and Technology (Formerly Thapar University) 2016  
38 26754 Mr. Shamik Das Male IIT Guwahati PhD IIT Guwahati 2016  
39 26809 Mr Mohan Mohan Male IIT Roorkee PhD scholar IIT Delhi 2017  
40 26820 Ms. Shreya Sharma Female IISER Mohali Second year Integrated PhD IISER Mohali Appeared  
41 - Chiranjit Ray - IIT Guwahati - - - -

 

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