Elliptic Curves, Elliptic Functions and Trancendence

Convener(s)

 
Name: R. Thangadurai Aprameyo Pal
Mailing Address: Professor H
Harish-Chandra Research Institute
Chhatnag Road, Jhunsi
Prayagraj 211019		 Reader F
Harish-Chandra Research Institute
Chhatnag Road, Jhunsi
Prayagraj 211019
Email: thanga at hri.res.in aprameyopal at hri.res.in

First four days, we shall cover the preliminaries required for the workshop themes. We shall introduce (1) Modular functions, mainly, modular j-function and its properties, its applications to space of meromorphic functions and Picard’s theorem. (2) Basic Elliptic curve properties and Complex multiplication theory, mainly, (3rd chapter of Cox book on ‘Primes of the form x2 +ny2 ’) (3) Introduction to Elliptic functions and its properties, Elliptic curve over C.

In the workshop part, we shall consider three themes: (1) The Schneider Lang Theorem: statement, corollaries and proof, The St ́ephanois Theorem on the transcendence of J(q) and Nesterenko’s Theorem: statement, corollaries and proof. (2) Gelfond’s transcendence criterion and its development with proof, Gelfond’s algebraic independence method: Small transcendence degree, Chudnovsky’s algebraic independence theorem (ω1, ω2, η1, η2) using: (i) the transcendence measure of π, (ii) Gelfond’s algebraic independence method combined with his zeros estimate and Elliptic analog of Brownawell-Waldschmidt theorem. The third theme is: Iwasawa theory for CM Elliptic curves.

Dates: 

Thursday, November 24, 2022 - 07:00 to Saturday, December 3, 2022 - 19:00

Venue: 

Venue Address: 

Chhatnag Road, Jhunsi, Prayagraj -211019
 

Venue State: 

Venue City: 

PIN: 

211019

Syllabus: 

 

Name of the Speaker with affiliation

Number of Lectures

Details Syllabu

R. Thangadurai
Professor HRI, Prayagraj

4 lectures of 1 hours 30 Minutes each

Introduction to Modular functions, Modular J-invariant function and its properties, Any meromorphic function is a rational function of J Picard’s theorem

Sohan Ghosh
Post-doc HRI, Prayagraj

4 lectures of 1 hours 30 Minutes each

Complex Multiplication

Veekesh Kumar
Post-doctoral fellow NISER, Bhubaneswarj

4 lectures of 1 hours 30 Minutes each

Introduction to Elliptic functions Elliptic curves over C

M.Waldschmidt Sorbonne
Université Institut Mathématique de Jussieu PARIS, FRANCE

6 lectures 1 hours 30 Minutes each

Introduction to Elliptic curves Stéphanois Theorem on the transcendence of J(q) and Nesterenko’s Theorem, corollaries, proof. The Schneider Lang Theorem, corollaries, proof.

K. Senthil Kumar
Reader NISER,Bhubaneswar

6 lectures 1 hours 30 Minutes each

Gelfond’s transcendence criterion and its development Gelfond’s algebraic independence method: Small transcendence degree Chudnovsky’s algebraic independence theorem (ω1 , ω2 , η1, η2) using: (i) the transcendence measure of π, (ii) Gelfond’s algebraic independence method combined with his zeros estimate Elliptic analog of Brownawell-Waldschmidt theorem

Aprameyo Pal
Reader HRI, Prayagraj

6 lectures of 1 hours 30 Minutes each

Iwasawa Theory for CM Elliptic curves

Time Table: 

 Time-table(with names of speakers and tutors):

Day/Time 09.15-10:45 10:45-11:00 11:00-12:30 12:30-14:00 14:00-15:30 15:30-15:50 15:50-16:50
24.11.2022 RT Tea SG Lunch VK Tea T(PT+RT)
25.11.2022 RT Tea SG Lunch VK Tea T(SG+AP)
26.11.2022 RT Tea SG Lunch VK Tea T(GP+VK)
27.11.2022 RT Tea SG Lunch VK Tea T(PT+RT)
28.11.2022 KS Tea AP Lunch MW Tea T(KS+GP)
29.11.2022 KS Tea AP Lunch MW Tea T(AP+SG)
30.11.2022 KS Tea AP Lunch MW Tea T(MW+VK)
01.12.2022 KS Tea AP Lunch MW Tea T(KS+GP)
02.12.2022 KS Tea AP Lunch MW Tea T(AP+SG)
03.12.2022 KS Tea AP Lunch MW Tea T(MW+VK)

 

Full forms for the abbreviations of Speakers and Tutors:

  • Speakers
    •  RT: R. Thangadurai (Professor, HRI, Prayagraj)
    •  AP: Aprameyo Pal (Reader, HRI, Prayagraj)
    •  SG: Sohan Ghosh (Post-doctoral fellow, HRI, Prayagraj)
    •  VK: Veekesh Kumar (Post-doctoral fellow, NISER, Bhubaneswar)
    •  KS: K. Senthil Kumar (Reader, NISER, Bhubaneswar)
    •  MW: M. Waldschmidt (Professor, Sorbonne Université, France)
  • Tutors
    •  PT: Prashant Tiwari (Post-doctoral fellow, HRI, Prayagraj)
    •  SG: Sohan Ghosh (Post-doctoral fellow, HRI, Prayagraj)
    •  GP: Gorek Prasad Sena (Research Scholar, NISER, Bhubaneswar)
    •  VK: Veekesh Kumar (Post-doctoral fellow, NISER, Bhubaneswar)
  • References
    •  D. Cox, Primes of the form X 2 + nY 2 .
    •  A. Seigal, Iwasawa Theory of Elliptic curves with CM.
    •  J. P. Serre, Course in Arithmetic.
    •  Tom Apostol, Modular functions and Dirichlet Series.
    •  K. Chandrasekaran, Elliptic functions.
    •  W. Stein and R. Shakarachi, Complex Analysis.
    •  E. T. Whittaker and G. N. Watson, Elliptic functions.
    •  M. Waldschmidt, Diophantine Approximation on Linear Algebraic groups.
    •  M. Ram Murty and P. Rath, Transcendental Number Theory.

 

Selected Applicants: 

 Acceptance email should be sent to mathoffice@hri.res.in on or before 9th November 2022.

Sr.n 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 43510 Mr. Vaibhav Kalia Male Indian Institute of Technology Ropar PhD student Motilal Nehru National Institute of Technology, Allahabad 2018  
2 43516 Dr. Lalit Vaishya Male Institute of Mathematical Sciences, Chennai Post Doctoral Fellow Banaras Hindu University (BHU), Varanasi 2014 19/05/2022
3 43555 Mr. Sushant Kala Male Institute of Mathematical Sciences, Chennai PhD I I T Ropar 2020  
4 43599 Mr. Shivansh Pandey Male National Institute Of Science Education And Research, Bhubaneswar PhD Banaras Hindu University, Varanasi 2019  
5 43649 Mr. Animesh Sarkar Male Indian Institute of Technology (BHU) Varanasi PhD Student University of North Bengal 2018  
6 43673 Mr Pronay Kumar Karmakar Male IISER Mohali PhD Tezpur University 2017  
7 43713 Mr Archit Agarwal Male IIT Indore PhD IIT Gandhinagar 2018  
8 43714 Ms. Meghali Garg Female IIT Indore PhD IIT Gandhinagar 2019  
9 43753 Mr Mohd Shahvez Alam Male IIT BHU PhD IIT Hyderabad 2019  
10 43756 Mr. Sampurna Pal Male ISI, Kolkata PhD ISI, Bangalore 2019  
11 43785 Dr Mohit Tripathi Male National Institute of Science Education and Research Research Associate-II M.Sc 2015 19/01/2021
12 43836 Ms Sanskruti Karnawat Female Not applicable(neither employed, nor studying) Not applicable UM-DAE Centre for Excellence in Basic Sciences, Mumbai 2022  
13 43862 Mr. Divyanshu Kala Male Indian Institute of Technology, Delhi PhD H.N.B. Garhwal University Srinagar Garhwal Uttarakhand / M.Sc. 2020  
14 43863 Ms. Akanksha Gupta Female IIT Delhi PhD IIT ISM Dhanbad 2021  
15 43864 Mr Mrityunjoy Charan Male National Institute of Science Education and Research, Bhubaneswar PhD Indian Institute of Technology Guwahati 2018  
16 43889 Mr Rajat Kumar Mishra Male IIT Gandhinagar PhD IISER, Kolkata 2019  
17 43901 Mr. Sudip Pandit Male Indian Institute of Technology Gandhinagar PhD Indian Institute of Technology Gandhinagar 2018  
18 43923 Dr. Ajit Singh Male Indian Institute of Technology Guwahati Research Associate Indian Institute of Technology Guwahati 2017 17/06/2022
19 44017 Mr. Tirtharaj Basu Male The Institute of Mathematical Sciences Integrated PhD The Institute of Mathematical Sciences    
20 44026 Mr. Dhananjay Kumar Male NIT Patna Ph.D. Department of Mathematics, Patna University 2015  
21 44102 Mr Vishakh Vasu Male Indian Institute of Science Education and Research. MS IISER Bhopal,BS-MS Appeared / Awaiting Result  
22 44115 Mr Sayan Ghosh Male Indian Statistical Institute PhD Indian Statistical Institute, Bangalore 2021  
23 44194 Ms Anitha G Female VIT CHENNAI CAMPUS PhD PRESIDENCY COLLEGE 2019  
  Local candidates            
1 43543 Ms Aparna Tripathi Female Harish Chandra Research Institute PhD University of Delhi 2018  
2 43552 Mr. Rohit Pokhrel Male Harish Chandra Research Institute, Prayagraj PhD Student Sikkim University 2019  
3 43583 Ms. Sudipa Das Female Harish-Chandra Research Institute PhD Ramakrishna Mission Vivekananda Educational and Research Institute 2021  
4 43705 Ms. Muskan Bansal Female Harish Chandra research institute PhD      
5 43877 Mr. Bhargab Das Male Harish-Chandra Research Institute PhD ISI Kolkata 2020  
6 43981 Mr Oais Ahmad Bhat Male Harish-Chandra Research Institute Ph.D student University of Kashmir 2019  
7 44010 Mr. Arpan Das Male Harish-Chandra Research Institute PhD student University of Hyderabad 2019  
8 44129 Mr. Shamik Das Male Harish-Chandra Research Institute PDF IIT Guwahati 2016 24/09/2021
  Waiting List Candidates            
1 43991 Mr. Amit Phogat Male Indian Institute of Technology Madras Msc Student Indian Institute of Technology Madras Appeared / Awaiting Result  
2 44103 Ms Vennela Pole Female Kerala School of Mathematics Mac Student Kerala School of Mathematics 2022  
3 44199 Mr Raman Rishi Male IIT Jodhpur MSc Student 2nd year   Appeared / Awaiting Result  

 

 

How to Reach: 

Click the following link for more details

http://www.hri.res.in/how-to-reach/

School Short Name: 

eceft

Last Date Application: 

Thursday, August 25, 2022

School Type: 

NCMW

Separate faculty form: 

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