Distinguished Lecture

Benedict Gross, Harvard University. The question of rational points on cubic curves has been of central interest in number theory for 350 years. About 50 years ago, Bryan Birch and Peter Swinnerton-Dyer formulated a precise conjecture for the rank of the group of rational points, in terms of the number of
solutions to the equation (modulo p) for all primes p. Gross will review the progress that has been made on this conjecture, and will discuss a method to bound the average rank.