National centre for maths workshop on elliptic curves begins at IISER Thiruvananthapuram

The workshop will help 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. 

The Indian Institute of Science Education and Research (IISER) Thiruvananthapuram in collaboration with the National Centre for Mathematics is organising a workshop on elliptic curves from April 3 to 15, 2023. The workshop is intended for PhD and postdoctrate students 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.  

The workshop will help 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, assistant professor, IISER Thiruvananthapuram, said, “The workshop on elliptic curves will provide an excellent opportunity for the participants. There are more than 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.” 

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 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 

The workshop 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. 

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