Needles in a Haystack: Elliptic Curves and a Lang--Trotter Conjecture

This page is for the keynote presentation by Dr. Nahid Walji.

Abstract

Elliptic curves are geometric objects defined by certain cubic equations. They have been studied by mathematicians for over a century, involving algebra, geometry, and number theory, and are the subject of several well-known conjectures. In this talk, I will discuss one in particular, conjectured by Lang and Trotter, that has resisted all attempts to prove it for almost half a century. We will begin by introducing elliptic curves and outlining their basic properties. Then we will discuss the research progress that has taken place so far towards this conjecture, up to where things stand in the present day.