In this talk we will define what is an elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were prominently featured in Wiles' proof of Fermat's last theorem, but there are many other problems that lead to a question about elliptic curves. We will discuss some of the open problems related to elliptic curves, and a number of conjectures, some of which are quite controversial!
Join us for refreshments at 3:30 on the second floor of Davis.