Elliptic Curves (2023)

Convener(s)

 
Name: Dr. Srilakshmi Krishnamoorthy Prof. Thangadurai Dr. Jayanta Manoharmayum:
Mailing Address: Assistant Professor,
Indian Institute of Science Education and Research Thiruvananthapuram		 Professor, Harish Chandra Research Institute, Allahabad Reader, Sheffield University
Email: srilakshmi at iisertvm.ac.in thanga at hri.res.in J.Manoharmayum at shef.ac.uk

Number theory is one of the oldest areas in mathematics, with problems that have remained unsolved for thousands of years and continue to fascinate people to this day. We have a rich tradition in number theory - the 2015 film ’The Man Who Knew Infinity’ brought the story of the self-taught genius Ramanujan to the masses. The mathematicians like Baudhayana who discovered what is commonly known as Pythagoras’s Theorem nearly three centuries before Pythagoras, or Brahmagupta who was the first to formalise the rules of arithmetic with the number zero. Fast forward a millennium or two and number theory now lies at the heart of the crypto systems that protect our bank accounts, and our personal data and form an integral part of modern life. The equations underlying these crypto systems are called elliptic curves. They remain objects of great mystery and are the subject of the million-dollar Millennium Prize Problem known as the Birch and Swinnerton-Dyer Conjecture. This conjecture draws links between the discrete or algebraic world of elliptic curves (in particular, a piece of data known as the ’rank’ of the curve), and the continuous or analytic world of some special functions called modular forms. The bridge provided by this conjecture allows mathematicians to transport knowledge between the two worlds. This workshop is intended for Ph.Ds and Postdocs to pursue their research in the area of elliptic curves.

Dates: 

Monday, April 3, 2023 - 19:00 to Saturday, April 15, 2023 - 19:00

Venue: 

Venue Address: 

IISER TVM, School of Mathematics, Vithura Campus, Maruthamalai PO 695551.

Venue State: 

Venue City: 

PIN: 

603103

Chrono Order: 

430

Syllabus: 

 Syllabus:

Name of the Speaker with affiliation Number of Lectures Syllabus/ Topics
Dr. Sarbeswar Pal IISER-TVM Lectures 4 hrs 30 mins
Tutorial - 1 hr		 Affine and Projective varieties : Rational Maps between varieties Algebraic Curves : Curves, Maps between curves, Divisors, Di↵erentials and Riemann Roch Theorem
R. Thangadurai Professor HRI, Prayagraj Lectures - 7 hrs
Tutorial - 1 hr		 The Geometry of Elliptic Curves : Elliptic Curves : Weierstrass Equations, The Group Law, Isogenies, Discriminant and multiplicative reduction, The Tate Module, The Weil Pairing The Endomorphism Ring The Automorphism Group, Formal Groups, Frey Curves
Neil Dummigan Professor Sheffield University, U.K. Lectures -6 hrs
Tutorial - 2 hrs		 Elliptic Curves over finite fields : Rational Points, The Weil Conjectures, The Endomorphism Ring, Hasse Invariant calculations.
Dr. Jayanta ManoharmayumUniversity, U.K. Sheffield Lectures - 6 hrs
Tutorial - 1 hr 2		 Elliptic Curves over C : The isomorphism E/C ⇠ = C⇤ /q Z, Tate Curve, Elliptic Integrals, Construction of Elliptic Functions Analytic and Algebraic Maps, Uniformization, The Lefschetz Principle Elliptic Curves over
Ram Murty Professor Queen’s University, Canada. Lectures - 6 hrs
Tutorial - 1 hr		 Global Fields: The Weak Mordell-Weil Theorem, The Kummer Pairing via Cohomology, The Descent Procedure, The Mordell-Weil Theorem over Q, Heights, Torsion Points, The Minimal Discriminant, The Rank of an Elliptic Curve, Szpiro Conjecture and ABC.
Dr. Narasimha Kumar, IIT Hyderabad. Lectures - 5 hrs
Tutorial - 1 hr		 Integral Points on Elliptic Curves - I: Diophantine Approximation, Distance Functions, Siegel Theorem,
Dr. Srilakshmi Krishnamoorthy IISER-TVM. Lectures - 1 hr 30 mins 
Tutorial - 1 hr		 Integral Points on Elliptic Curves - II: Shafarevich Theorem, Roth Theorem.
Dr. Shaunak Deo IISc, Bangalore. Lectures - 6 hrs Tutorial - 1 hr Computing the Mordell-Weil Group: Examples, Twisting-General Theory Homogeneous Spaces, The Selmer and Shafarevich-Tate Groups Twisting-Elliptic Curves.
Kalyan Chakraborty Professor KSOM, Calicut. Lectures - 6 hrs Tutorial - 1 hr 3 Algorithmic Aspects of Elliptic Curves: Elliptic Curve Factorization Algorithm (by Lenstra), Elliptic Curve Cryptography, Pairing-Based Cryptography, Applications to Cryptography, Double-and-Add Algorithms, Counting the Number of Points in E(Fq ), Solving the ECDLP: The General Case and special case, Computing the Weil Pairing, The Tate-Lichtenbaum Pairing.
Lawrence Washington Professor University of Maryland, USA. Lectures - 6 hrs Introduction to Iwasawa Theory: Basic facts, The structure of ⇤-modules, Iwasawa’s theorem, consequences, Logarithmic derivatives, Local units modulo cyclotomic units.
Sujatha Ramdorai Professor University of British Columbia, Canada Lectures - 6 hrs Tutorial - 1 hr Iwasawa modules for elliptic curves: Bloch–Kato Selmer groups, Selmer structures,The extension F1 /F , Selmer groups over F1 , Control theorems, Construction of the p-adic L-functions, Some p-adic Measure Theory, Formulation of the Main Conjecture.
Dr. Bharathwaj Palvannan IISc, Bangalore. Lectures - 6 hrs  Tutorial - 1 hr p-adic L-functions of elliptic curves : Periods, modular symbols, measures, algebraicity and integrality of L-values.

Time Table: 

 Week 1

Time/ Day 03/04 04/04 05/04 06/04 07/04 08/04
09:30- 11:00 SP SP RT RT LW LW
11:00- 11:30 Tea Tea Tea Tea Tea Tea
11:30- 13:00 RT RT JM JM JM JM
13:00- 14:30 Lunch Lunch Lunch Lunch Lunch Lunch
14:30- 16:00 SP ND ND ND ND NK
16:00- 16:30 Tea Tea Tea Tea Tea Tea
16:40- 17:40 RT+SKP +SB SP+SKP +SB ND+SKP +SB JM+SKP +SB ND+SKP +SB NK+SKP +SB
18:00- 19:00 LW LW LW RT NK NK

 Week 2

Time/ Day 10/04 11/04 12/04 13/04 14/04 15/04
09:00- 10:30 SR SR SR SK RM RM
10:30- 11:00 Tea Tea Tea Tea Tea Tea
11:00- 12:30 SR SD SD RM SD SD
12:30- 14:00 Lunch Lunch Lunch Lunch Lunch Lunch
14:00- 15:30 NK BP BP BP BP RM
15:30- 16:00 Tea Tea Tea Tea Tea Tea
16:00- 17:00 KC KC KC KC KC KC
17:10- 18:10 KC+TD +RV BP+TD +RV SD+TD +RV RM+TD +RV SK+TD +RV SR+TD +RV

 

Full forms for the abbreviations of Speakers and Tutors

speakers:

  • SP: Dr. Sarbeswar Pal
  • RT: Prof. Ravindranathan Thangadurai
  • ND: Prof. Neil Dummigan
  • JM: Dr. Jayanta Manoharmayum
  • RM: Prof. Ram Murty
  • SK: Dr. Srilakshmi Krishnamoorthy
  • SD: Dr. Shaunak Deo
  • KC: Prof. Kalyan Chakraborty
  • NK : Dr. Narasimha Kumar
  • LW: Prof. Lawrence Washington
  • SR: Prof. Sujatha Ramdorai
  • BP: Dr. Bharathwaj Palvannan

Tutors :

  • SKP: Mr. Sunil Pasupulati (Final year PhD student at IISER-TVM)
  • SZ: Dr. Ravitheja Vangala (Postdoctoral fellow, IISc, Bangalore)
  • SB: Dr. Subham Bhakta (Visitor, IISER-TVM)
  • TD: Dr. Tarun Dalal (Postdoctoral Fellow, HRI, Allahabad).

References

  • Joseph H. Silverman, The arithmetic of elliptic curves, second ed., Graduate Texts in Mathematics, vol. 106, Springer, Dordrecht, 2009.
  • J. Coates and R. Sujatha, Cyclotomic fields and zeta values, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2006.
  • Lawrence C. Washington, Introduction to cyclotomic fields, second ed., Graduate Texts in Mathematics, vol. 83, Springer-Verlag, New York, 1997.
  • Lawrence C. Washington, Elliptic curves, second ed., Discrete Mathematics and its Applications (Boca Raton), Chapman & Hall/CRC, Boca Raton, FL, 2008, Number theory and cryptography.
  • Ralph Greenberg, Introduction to Iwasawa theory for elliptic curves, Arithmetic algebraic geometry (Park City, UT, 1999), IAS/Park City Math. Ser., vol. 9, Amer. Math. Soc.,Providence, RI, 2001, pp. 407–464.

Selected Applicants: 

Instructions for NCM Selected List:

  1. Confirm participation by 21st of March, 2023 by sending an email to  the following id: ncmw23@iisertvm.ac.in
  2. We will not send any separate emails to the selected participants. For official leave purposes, one may take the printout of the selected participants.

Selected Applicants

Sr.n SID Full Name Gender Affiliation Position in College/ University University/ Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A
1 45983 Mr Pankaj Patel Male BITS Pilani, Hyderabad Campus PhD IIT Guwahati 2019
2 45984 Mr. Om Prakash Male Kerala school of mathematics Ph.D. Kerala school of mathematics 2022
3 45993 Mr. Ganesh Jayantrao Dharmadhikari Male IIT GANDHINAGAR ARYABHATA - HoMI FELLOW IISER TVM 2020
4 46015 Mr Mohd Shahvez Alam Male IIT BHU PhD IIT Hyderabad 2019
5 46036 Mr. Vidit Das Male Rajiv Gandhi Institute of Petroleum Technology PhD IISER Bhopal 2019
6 46039 Mr Rajat Kumar Mishra Male IIT Gandhinagar PhD IISER, Kolkata 2019
7 46133 Ms. Dipanjana Sheet Female Indian Institute of Technology Hyderabad PhD Indian Institute of Technology Hyderabad 2021
8 46136 Mr. Rakesh Kumar Male Indian Statistical Institute Kolkata PhD Indian Institute of Technology Bhubaneswar 2018
9 46140 Mr. Suraj Rajendra Kulkarni Male The Institute of Mathematical Sciences Integrated PhD Student IMSc, Chennai Appeared
10 46143 Mr. Shubham Jaiswal Male KSCSTE-Kerala School of Mathematics Integrated MSc-Phd KSCSTE-Kerala School of Mathematics Appeared
11 46224 Mr. Rudranarayan Padhy Male National Institute of Technology, Calicut Project fellow in Department of Mathematics,NITC Khallikote University 2018
12 46275 Dr Mohit Tripathi Male National Institute of Science Education and Research Post-doctoral Fellow M.Sc 2015
13 46335 Mr Archit Agarwal Male IIT Indore PhD IIT Gandhinagar 2018
14 46343 Mr. Debajyoti De Male IIT MADRAS PhD RAMAKRISHNA MISSION VIVEKANANDA EDUCATIONAL AND RESEARCH INSTITUTE 2021
15 46344 Ms. Sulakashna Sulakashna Female Indian Institute of Technology Guwahati Research Scholar Indian Institute of Technology Guwahati 2020
16 46346 Ms H Laxmi Female Indian Institute of Technology Guwahati PhD Student Indian Institue of Technology Guwahati 2020
17 46349 Ms Malavika E Female Indian Institute of Science Education and Research (IISER), Berhampur, Orissa. PhD Pondicherry University 2019
18 46367 Ms Khyati . . Female IIIT-D PhD Bananas Hindu University 2018
19 46405 Mr. Laba Sa Male University of Hyderabad Ph.D. Scholar Sambalpur University 2014
20 46412 Ms. Mahinshi . Female Jawaharlal Nehru University, New Delhi PhD IISER Mohali 2019
21 46417 Mr. Prabhat Kumar Mishra Male Indian Institute of Technology Jammu PhD Indian Institute of Technology Guwahati 2021
22 46436 Mr. Rishabh Agnihotri Male Indian Institute of science, Bangalore Post-doc Fellow IIT Kanpur, Kanpur 2017
23 46447 Ms Arathy Venugopal Female Indian Institute of Science Education and Research, Tirupati PhD Indian Institute of Science Education and Research, Tirupati 2021
24 46448 Mr. Sushant Kala Male The Institute of Mathematical Sciences, Chennai PhD IIT Ropar 2020
25 46468 Mr. Sridhar T Male IIITDM Kancheepuram, Chennai. PhD Bharathidasan University, Tiruchirappalli - 620024, Tamil Nadu. 2018
26 46481 Mr. Subhajit Mukherjee Male IISER Thiruvananthapuram integrated PhD IISER Thiruvananthapuram Appeared
27 46624 Mr. Suraj Panigrahy Male Indian Institute of Technology Bombay PhD Indian Institute of Technology Guwahati 2020
28 46645 Ms Amrutha C Female SRM University AP PhD Central University of Kerala 2020
29 46646 Mr. Vaibhav Kalia Male Indian Institute of Technology Ropar PhD Motilal Nehru National Institute of Technology, Prayagraj 2018
30 46716 Mr. Shubham Gupta Male Harish-Chandra Research Institute Ph.D. student Indian Institute of Technology Kanpur 2018
31 46755 Mr Muneeswaran R Male IISER Thiruvananthapuram PhD Central University Of Kerala 2020
32 46771 Mr. Ashutosh Suresh Jangle Male Indian Institute of Science, Bangalore PhD Indian Institute of Science Education and Research, Pune 2021
33 46820 Ms. Devi S Female Central University of Tamil Nadu PhD Student Central University of Tamil Nadu ( Integrated M.Sc ) 2021
  Self-Sponsors List
   Instructions for the Self-Sponsors List:
  1. The charge for food and accommodation per day is  Rs. 600 per student. A total of Rs. 7,800/- for 13 days. Bills will be provided so that the participants can be reimbursed this amount from their contingency grant, if any, in their respective institutes.
  2. The interested candidates in this list need to confirm their participation by sending an email to the following id: ncmw23@iisertvm.ac.in
1 45982 Mr. Rohit Pokhrel Male Harish Chandra Research, Institute Ph.D. Sikkim University 2019
2 45998 Mr. Animesh Sarkar Male Indian Institute of Technology (BHU) Varanasi Ph.D. Student University of North Bengal 2018
3 45999 Ms. Muskan Bansal Female Harish-Chandra Research Institute PhD National Institute of Technology, Warangal 2021
4 46027 Ms. Sudipa Das Female Harish-Chandra Research Institute PhD RKMVERI 2021
5 46042 Mr. Vinodkumar Ghale Male BITS - Pilani, Hyderabad Campus Ph.D. student University Of Hyderabad 2016
6 46134 Mr Manas Jana Male Indian Institute of Technology Kharagpur PhD Ramakrishna Mission Vivekananda Educational and Research Institute 2020
7 46154 Mr. Akhil Surendran Male I.I.T GANDHINAGAR PhD CENTRAL UNIVERSITY OF TAMILNADU 2019
8 46163 Mr. Sudip Pandit Male IIT Gandhinagar PhD IIT Gandhinagar 2018
9 46215 Mr. Ajay Prajapati Male Indian Institute of Science, Bangalore Ph.D. Indian Institute of Technology, Kanpur 2022
10 46306 Dr. Lalit Vaishya Male The Institute of Mathematical Sciences, Chennai India Post Doctoral Fellow BANARAS HINDU UNIVERSITY VARANASI 2014
11 46336 Ms. Meghali Garg Female IIT Indore Ph.D. IIT Gandhinagar 2019
12 46339 Dr. Ajit Singh Male Indian Institute of Technology Guwahati Research Associate Indian Institute of Technology Guwahati 2017
13 46352 Dr. Jaitra Chattopadhyay Male Indian Institute of Technology Guwahati Post-Doctoral Fellow Ramakrishna Mission Vidyamandira 2015
14 46389 Dr. Karthick Babu C G Male ISI- Bangalore Post doctoral fellow M.Sc. Maths 2014
15 46394 Ms Meenu Meenu Female Kerala school of mathematics PhD Central University of Rajasthan, Rajasthan 2021
16 46423 Mr. Shamik Das Male Harish-Chandra Research Institute Post Doctoral Fellow IIT Guwahati 2016
17 46424 Mr. Krishnarjun Krishnamoorthy Male Harish-Chandra Research Institute OhD Central University of Tamil Nadu 2018
18 46429 Mr Subhasis Panda Male IIT MADRAS Phd University of Hyderabad 2015
19 46437 Mr. Mohit Mishra Male IIT Guwahati NBHM Post Doctoral Fellow IIT Madras 2017
20 46444 Mr. Kushal Bhowmick Male Harish Chandra Research Institute. PhD Student. Indian Statistical Institute 2017
21 46537 Dr. Rakhi Pratihar Female Indraprastha Institute of Information Technology Delhi Postdoctoral Researcher Jadavpur University 2016
22 46541 Mr. Akshay Ankush Yadav Male University of Delhi PhD Student Indian Institute of Science Education and Research, Thiruvananthapuram 2019
23 46544 Mr. Ajay Dabral Male Department of Mathematics, University of Delhi PhD Student University of Delhi 2017
24 46752 Mr. Sanjay Kumar Male Scientific Analysis Group, DRDO Scientist-E Chaudhary Charan Singh University Campus Meerut 2005
25 46753 Mr. Arindam Mandal Male Scientific Analysis Group, DRDO, Delhi Scientist-C IIT Madras 2015
26 46792 Ms. Swarnalipa Datta Female Indian Statistical Institute, Kolkata Senior Research Fellow Indian Institute of Science, Bangalore 2020
27 46817 Dr. Subramani Muthukrishnan Male Indian Institute of Information Technology D&M, Chennai Asst. Professor University of Madras 2009
28 46831 Ms. Khushboo Yadav Female Jamia millia Islamia New Delhi PhD Baba saheb bhimrao ambedkar University Lucknow 2021
29 46837 Mr Sai Sanjeev Male Indian Institute of Science student    

  Waiting  List

Instructions for Waiting List:

  1. Waiting list will move in the above order only as and when some cancellation of participation in NCM Selected list.
  2. We shall send intimate the waiting list candidate by email, once any cancellation in the main list.
1 46208 Ms. Shivani Goel Female Indraprastha Institute of Information Technology, Delhi PhD Chaudhary Charan Singh University, Meerut 2018
2 46334 Mr. Ritoprovo Roy Male Kerala School of Mathematics Integrated MSc - PhD student Kerala School of Mathematics Appeared
3 46420 Mr. Mahesh Kumar Ram Male IISER Berhampur PhD Vinoba Bhave University, Hazaribag 2016
4 46501 Mr. Nimish Kumar Mahapatra Male IISER Berhampur PhD IIT Guwahati 2016
5 46586 Mr. Shubham Hooda Male Jawaharlal Nehru University PhD National Institute of Technology, warangal 2018
6 46685 Mr. Bittu . Male IIITD PhD Indian Institute of Technology Roorkee 2019
7 46725 Mr. Shivansh Pandey Male NISER, Bhubaneswar PhD Banaras Hindu University, Varanasi 2019
8 46840 Mr. Aishik Chattopadhyay Male Ramakrishna Mission Vivekananda Educational and Research Institute PhD Pondicherry University 2018
9 46197 Mr. Subhendu Pramanick Male Kerala School of Mathematics Int. M.Sc-Ph.D student Kerala School of Mathematics Appeared

 

 

How to Reach: 

How to reach

School Short Name: 

ec

Last Date Application: 

Monday, August 15, 2022

School Type: 

NCMW

Separate faculty form: 

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