# Math 990, Advanced Topics in Elliptic Curves - Fall 2004

# Nigel Boston

## Contact Information

303 Van Vleck Hall
Telephone: 263-4753.

E-mail: *boston@math.wisc.edu*

Homepage

Office Hours: Tuesdays, 10-11 (in 303 VV), Wednesdays 11-12 (in 3619 EH), Thursdays 2:20-3:20 (in 303 VV).

## Sections

- Lecture: TR 12:20-1:10, 901 Van Vleck.

## Useful Web Materials

Elliptic curves resources

Elliptic curve resources

Elliptic curve research articles

Elliptic curves and cryptology links

Elliptic curve rank records

List of useful elliptic curve links

Rusin's elliptic curve links

More elliptic curve links
## Course Description

We will continue the study of elliptic curves begun in spring 2004. I shall
lecture for 3 weeks on some advanced but preparatory material, followed by
each person registered lecturing for a week.
## More Detailed Plan

- Sept 7 and 9: Nigel Boston, Tate curves and local Galois representations.
- Sept 14 and 16: Nigel Boston, Formal groups and elliptic curves.
- Sept 21 and 23: Nigel Boston, Galois cohomology, Selmer groups, and Tate-Shafarevich groups.
- Sept 28 and Oct 5: Andrew Shallue, Profinite groups.
- Oct 7 and 12: David Dueber, The congruent number problem.
- Oct 14 and 19: Jeremy Rouse, Coates-Wiles results on Birch - Swinnerton-Dyer conjecture for CM elliptic curves.
- Oct 21 and 26: Ben Kane, Ribet's raising and lowering the level.
- Oct 28 and Nov 2; Sharon Chuba-Garthwaite, Using elliptic curves to solve A^4 + B^4 + C^4 = D^4.
- Nov 4 and 9: Jayce Getz, Arakelov theory of elliptic curves.
- Nov 11 and 16: Patrick Rault, The elliptic curve of conductor 5077 and Gauss's class number problem.
- Nov 18 and 23: Chris Holden, Serre's conjecture on mod p Galois representations.
- Nov 30: Nigel Boston, Group schemes.
- Dec 2 and 7: Karl Mahlburg, Elliptic curve cryptography, in particular using CM to get good curves.
- Dec 9 and 14: Haluk Sengun, Continuation of Serre's Inventiones Math 15 paper.
- Dec 16: Nigel Boston, Group schemes.