Math 990, Advanced Topics in Elliptic Curves - Fall 2004

Nigel Boston

Contact Information

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

Course Description

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.