Elliptic Curves come under a relatively nascent area of mathematics known as Algebraic Geometry. They are by no means ellipses. They have come to be more widely known because of their use in the proof of the famous Fermat’ s Last Theorem. They bring together areas of Number Theory, Algebra and Geometry and have a wide range of applications – Cryptography being one of them. The questions I will address deal with the properties of finding a certain kind of points on these curves which are closely linked to the cryptographic applications.

**Smriti Angara**, ’07 Hyderabad, India

Major: Politics

Sponsors: James Freeman and Stephen Bean