National Centre for Mathematics Workshop on Elliptic Curves starts at IISER Thiruvananthapuram
Indian Institute of Science Education and Research Thiruvananthapuram (IISER TVM) in collaboration with the National Centre for Mathematics is organizing a workshop on Elliptic Curves from 3rd to 15th April 2023. This workshop is intended for Phds and Postdocs to pursue their research in the area of elliptic curves. Elliptic curve theory links many branches of mathematics, including algebraic geometry, number theory, complex analysis, and representation theory. A vast amount of research is being conducted in this area.
The workshop will impact the students to directly interact and exchange ideas with the experts in arithmetic geometry and Iwasawa theory. It would also motivate the participants to conduct research in cryptography and other topics related to elliptic curves.
Speaking about the event, Dr. Srilakshmi Krishnamoorthy, Event Organizer, and Assistant Professor, IISER Thiruvananthapuram, said, “The NCM Workshop on Elliptic Curves will provide an excellent opportunity for the participants. There are 60+ participants from various Institutes in India, including scientists and faculties. There are also four tutors who will conduct tutorial sessions to provide hands-on experience in computations.”
The faculty further 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”.
Elliptic curves possess intriguing geometric properties and can be used to solve number theory problems. After more than three centuries of effort by mathematicians, Andrew Wiles proved Fermat’s last theorem by using the modularity of elliptic curves. In cryptography, elliptic curves can be used to develop public-key encryption schemes that are resistant to quantum computer attacks. These schemes are widely employed in secure communication protocols as well as financial transactions.
Key topics which would be covered in the workshop will include:
➢ Basic Algebraic Geometry
➢ The Geometry of elliptic curves
➢ Elliptic curves over finite, local and global fields
➢ BSD & ABC conjectures
➢ Integral points on the elliptic curves
➢ Algorithmic aspects of elliptic curves
➢ Elliptic curve cryptography
➢ Iwasawa theory, p-adic functions for elliptic curves
NCMW on Elliptic Curves will provide an opportunity to the 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.
The event will host multiple experts and eminent personalities in the field of Arithmetic Geometry and Iwasawa Theory, from India and abroad, as the guest lecturers. Key speakers include:
➢ Padma Shri Prof. Sujatha Ramdorai – University of British Columbia, Canada
➢ Prof. R. Thangadurai – Harish Chandra Research Institute, Prayagraj
➢ Prof. Neil Dummigan – Sheffield University, U.K.
➢ Prof. Ram Murty – Queen’s University, Canada
➢ Prof. Kalyan Chakraborty – Kerala School of Mathematics, Calicut.
➢ Prof. Lawrence Washington – University of Maryland, USA.
➢ Dr. Jayanta Manoharmayum – Sheffield University, U.K.
➢ Dr. Shaunak Deo – Indian Institute of Science, Bangalore
➢ Dr. Bharathwaj Palvannan – Indian Institute of Science, Bangalore
➢ Dr. Sarbeswar Pal – IISER Thiruvananthapuram
➢ Dr. Narasimha Kumar – Indian Institute of Technology Hyderabad
➢ Dr. Srilakshmi Krishnamoorthy – IISER Thiruvananthapuram