Computational Algebra Seminar: Voight -- Ranks of elliptic curves

Speaker: John Voight (Sydney)
Title: Ranks of elliptic curves
Time & Place: 15.00-16.00, Thursday 9 October, SMRI Seminar Room
Abstract:
Elliptic curves lie at the intersection of many areas of mathematics and remain 
central to modern 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 up to 
torsion. A fundamental question, going back to Poincaré, remains unresolved: can 
the rank be arbitrarily large? 
In this talk, we present computations and data, a statistical model and heuristic 
framework to guide our expectations, and outliers that challenge these assumptions. 
This is joint work with Jennifer Park, Bjorn Poonen, and Melanie Matchett Wood.