IISER Thiruvananthapuram organises national centre for maths workshop on elliptic curves

NEW DELHI: The Indian Institute of Science Education and Research Thiruvananthapuram (IISER TVM) has organised a workshop on elliptic curves in collaboration with the National Centre for Mathematics from April 3 to 15, 2023. The workshop will enable students to directly interact and exchange ideas with experts in geometry and Iwasawa theory.

The IISER TVM workshop is intended for PhD and post doctorate students to pursue their research in the area of elliptic curves. The workshop will also provide researchers and practitioners in the fields of mathematics and cryptography to learn the tools to explore the latest developments in elliptic curve theory and its applications to these disciplines.

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The key topics that will be covered at the event include basic algebraic geometry, geometry of elliptic curves, elliptic curves over finite, local and global fields, BSD and ABC conjectures, integral points on the elliptic curves, algorithmic aspects of elliptic curves, elliptic curve cryptography, Iwasawa theory and p-adic functions for elliptic curves.

Over 60 participants from various institutes in India, including scientists and faculties are expected to attend the event. In addition to this, there are also four tutors who will be conducting tutorial sessions to provide hands-on experience in computations.

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Speaking about elliptic curves, IISER Thiruvananthapuram event organiser and assistant professor Srilakshmi Krishnamoorthy, said: "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 formalize 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 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".