Ranks of elliptic curves

Prof. Bjorn Poonen

MIT

https://math.mit.edu/~poonen/

Abstract

Elliptic curves are simplest varieties whose rational points are not fully understood, and they are the simplest projective varieties with a nontrivial group structure. In 1922 Mordell proved that the group of rational points on an elliptic curve is finitely generated. We will survey what is known and what is believed about this group.

Speaker

Bjorn Poonen is a number theorist and algebraic geometer, a member of American Academy of Arts and Sciences.

He is interested in solving polynomial equations with the requirement that the coordinates of the solutions be either integers (like -37) or rational numbers (like -3/5). Such problems have been studied for their intrinsic interest since the time of the ancient Greeks. Starting in the 20th century, they found unforeseen applications, in cryptography (e.g., to make online transactions secure) and the theory of error-correcting codes (e.g., to encode data on a DVD in such a way that it can be recovered even if errors are introduced). His research focuses not on these applications, but rather on the fundamental mathematics underlying and surrounding them. He also works on the “dark side” of mathematics, to prove that certain problems are unsolvable in a precise sense.

Thursday, Nov. 21, 2024

9:00–10:30 am ET

22:00-23:30 (Beijing Time)