A working seminar on Elliptic Curves and related Topics

· When and where? Every Wednesday 4:10-5p.m. at 290 Carver Hall.

· What are elliptic curves? http://en.wikipedia.org/wiki/Elliptic_curves

· Besides topics on elliptic curves, we will discuss elliptic functions, algebraic curves, and possibly modular forms.

Fall 2008 seminar schedule:

Date	Speaker	Title	Abstract
9-17-08	Geoff Tims	Introduction to elliptic curves (part 1)
9-24-08	Geoff Tims	Introduction to elliptic curves (part 2)
10-1-08	Chris Kurth	Elliptic functions I
10-8-08	Chris Kurth	Elliptic functions II
10-22-08	Ling Long	Isogeny	We define morphisms between smooth curves, ramification degrees of modphisms at given points, and isogenies between elliptic curves.
10-29-08	Ling Long	Isogeny II	We define dual isogenies, consider basic properties of isognies and the endomorphism rings of elliptic curves.
11-5-08	Tim Huber	Torsion points of elliptic curves I
11-12-08	Tim Huber	Torsion points of elliptic curves II
11-19-08	Chris Kurth	Schoof's algorithm	We discuss an efficient algorithm for counting the number of points on an elliptic curve defined over a finite field.
12-3-08	Ling Long	Isogeny III	We discuss endomorphism rings of elliptic curves over different fields, complex multiplications.
12-10-08	Ling Long	Supersingular elliptic curves	Supersingular elliptic curves over finite fields will be defined and properties of these elliptic curves will be discussed.
12-17-08	Ling Long	Supersingular elliptic curves II