Kieval Lecture: Elliptic Curves are not Ellipses (and that’s a good thing).

Elliptic curves have long occupied a central place of intrigue in mathematics, as a very special class of curves whose landscape touches aspects of number theory, group theory, algebraic geometry, complex analysis, cryptography, etc.  The fact that elliptic curves are not ellipses is what allows all of this to happen! In this talk, we will start from the beginning of the path of elliptic curves and demonstrate their fundamental arithmetic properties and geometric interpretations, and show where the name elliptic comes from. Then, we will discuss a very intriguing result on elliptic curves known as Manin’s Unity, which shows that certain areas of the elliptic curve landscape, which appear to be very distant from each other, are actually closely intertwined. This talk will be accessible to undergraduates.