NCMW - Elliptic Curves, Elliptic Functions and Trancendence

Speakers and 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.

 

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