Murmurations of elliptic curves

Abstract: This talk will review some data scientific experiments involving arithmetic objects, focusing mainly on averaging the Dirichlet coefficients associated to elliptic curves within fixed conductor ranges. In particular, a surprising oscillation that appears in these averages will be discussed. This talk is based on work with He, Lee, and Oliver.

machine learningmathematical physicsalgebraic geometryalgebraic topologynumber theory

Audience: researchers in the topic

DANGER2: Data, Numbers, and Geometry