MAT 7470

Dan Isaksen
Winter 2007
Wayne State University

The topic of the course will be elliptic curves. This topic is relevant in several different mathematical fields, including number theory, algebraic geometry, algebraic groups, algebraic topology, cryptography, and even the classical theory of integration.

The course will not be organized in the usual standard lecture/homework/exam format. Rather, students will be responsible for giving the bulk of the lectures. My job will be to help students prepare their presentations. We will also spend class time discussing and presenting the homework problems.

The goal of the course is for students to practice learning directly from books. This is a skill that all graduate students need to learn eventually. Another goal is for students to practice presenting advanced material. And the third goal is for students to learn something about elliptic curves.

The text will be The Arithmetic of Elliptic Curves by Joseph Silverman, Graduate Texts in Mathematics 106, Springer. We will start with Chapter I, and we'll work our way through until we run out of time.

This class is for students who want to participate. It's not for students who are looking for a passive experience. In terms of prerequisites, MAT 7400 should suffice.

Schedule

M 1/8/07: Dan: An Overview of Elliptic Curves; Housekeeping.

W 1/10/07: Sean: Weierstrass equations (III.1).

W 1/17/07: Sean: Weierstrass equations (III.1).

M  1/22/07: Armira: Elliptic curves in characteristics 2 and 3 (App. A); The group law (III.2).

W 1/24/07: Armira: The group law (III.2).

M 1/29/07: Tung: The automorphism group (III.10); Elliptic functions (VI.2).

W 1/31/07: Tung: Elliptic functions (VI.2). 

M 2/5/07: Hung: Construction of elliptic functions (VI.3).

W 2/7/07: Hung: Construction of elliptic functions (VI.3).

M 2/12/07: Hung: Construction of elliptic functions (VI.3).

W 2/14/07: Xianfen: Affine varieties (I.1).

M 2/19/07: Evgeny: Projective varieties (I.2).

W 2/21/07: Evgeny: Projective varieties (I.2); Armira: Maps between varieties (I.3).

M 2/26/07: Doug Ravenel: Elliptic curves: what they are, why they are called elliptic, and why topologists like them (2:45pm).

T 2/27/07: Doug Ravenel: An introduction to elliptic cohomology and topological modular forms (2pm).

W 2/28/07: Doug Ravenel: Elliptic curves: what they are, why they are called elliptic, and why topologists like them (2:45pm).

Th 3/1/07: Doug Ravenel: Toward higher chromatic analogs of elliptic cohomology and topological modular forms (2pm).

M 3/5/07: Armira: Maps between varieties (I.3); Hung: Curves (II.1).

W 3/7/07: Hung: Curves (II.1); Tung: Maps between Curves (II.2).

M 3/19/07: Tung: Maps between Curves (II.2).

W 3/21/07: Tung: Maps between Curves (II.2); Sean: Divisors (II.3).

M 3/26/07: Sean: Divisors (II.3); Dan: Differentials (II.4).

W 3/28/07: Dan: Differentials (II.4).

M  4/2/07: Dan: Differentials (II.4), The Riemann-Roch Theorem (II.5).

W 4/4/07: Dan: The Riemann-Roch Theorem (II.5); Xianfen: III.1.5.

M  4/9/07: Xianfen: III.1.6, III.3.1.

W 4/11/07: Evgeny: Elliptic Curves (III.3).

M 4/16/07: Sean: Formal Groups (IV); Course Evaluations.

W 4/18/07: Sean: Formal Groups (IV); Dan: Isogenies (III.4).

M 4/23/07: Dan: Isogenies (III.4).


Email: isaksen at math.wayne.edu