NCMW - Elliptic Curves (2023)

Venue: IISER, Thiruvananthapuram

Dates: 3 Apr 2023 to 15 Apr 2023


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 thanga at J.Manoharmayum at

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.