Ranks of elliptic curves

About the lecture

Elliptic curves reside at the intersection of many areas of mathematics and remain at the heart of number theory. The rank of an elliptic curve over the rational numbers measures the size of its group of rational points: intuitively, it counts the number of independent points needed to generate all rational solutions. A fundamental question remains: do curves of arbitrarily large rank exist?

In this talk, we present computations, a statistical model that provides a heuristic to guide our expectations, and outliers that challenge them. The talk is aimed at students and researchers interested in the intersection of pure and computational mathematics.

About the speaker

John Voight is a Professor of Mathematics at the University of Sydney and leader of the Magma computational algebra group. His research focuses on number theory and arithmetic geometry, with expertise in algorithmic and computational aspects. He received his PhD from the University of California at Berkeley in 2005, holding  positions at the University of Vermont and Dartmouth College before moving to Sydney in 2024. He was recently named a Fellow of the American Mathematical Society.

Schedule

1-2pm: Presentation by Prof. John Voight in Room 4082, Anita B. Lawrence Centre, UNSW.
2pm: Light refreshments.

Venue

The lecture will be presented in Room 4082/3 on level 4 of the Anita B. Lawrence Centre at UNSW (ref: H15 on the UNSW campus map, opens in a new window). Light refreshments will be served in Room 3082 following the talk.

Frontiers in Fundamental Mathematics Research Nexus

This event is presented by the UNSW School of Mathematics and Statistics and is part of our Frontiers in Fundamental Mathematics Research Nexus series, which aims to highlight fundamental research in the mathematical sciences, with an emphasis on the significance and impact of fundamental mathematics to a diverse range of areas within mathematics and beyond.
Learn more about the Nexus Program, opens in a new window.