Computational Algebra Seminar: Donnelly -- The method of descent: determining the rational points on elliptic curves

Speaker: Steve Donnelly
Title: The method of descent: determining the rational points on elliptic curves
Time & Place: 3:05-4pm, Thursday 3 June, Carslaw 535

Abstract:
I’ll begin a short series of talks outlining the theory of the
descent algorithms implemented in Magma, whose purpose is to
determine the group of rational points on a given elliptic curve.

(For elliptic curves over Q, we have 2-descent, 4-descent and now
full-fledged 8-descent; alongside this, we have 3-descent
and now 6- and 12-descent.  Complementary to 4- and 8-descent,
we have the Cassels-Tate pairing for 2- and 4-coverings.)

The first talk will describe 2-descent from an elementary
point of view, so it will be accessible and will lay the
foundations for the remaining talks.