Math 847, A Proof of Fermat's Last Theorem - Spring 2013
303 Van Vleck Hall
Office Hours: Tuesdays 10:45-12:15 (in 303 VV), Wednesdays 1:30-3:00 (in 3619 EH).
- Lecture: TR 9:30-10:45, B129 Van Vleck.
Useful Web Materials
To Get a Grade
(1) Take notes one class and produce a TeX version
(2) Write a class project (10 to 20 pages) on one of the topics listed below or something of your own choice
(3) Give a 10 to 15 minute presentation to the class and to me on the same project
1. The abc conjecture.
2. Fermat-like equations.
3. Examples of Serre's conjecture and applications.
4. Families of elliptic curves with given mod p Galois representation.
5. More on Ribet's raising and lowering the level.
6. Group schemes and work of Khare et al.
7. More cases of the Fontaine-Mazur conjecture.
8. Kummer's work on regular primes.
9. Framed deformations.
10. Further properties of modular curves.
11. Profinite group theory.
13. The presentation of the absolute Galois group of the p-adics.
14. Explicit examples of modular curves.
15. Comparing the different constructions of universal deformation rings.
16. Fermat's last theorem over other rings (number rings, function fields, etc.).
17. Congruences of modular forms and Galois representations.
18. The modularity of mod 3 Galois representations.
19. Even Galois representations.
20. Brumer-Kramer proof of non-existence of elliptic curves of certain conductors.
21. Faltings-Serre method for finding all elliptic curves of small conductor.
22. Modular symbols and calculating with elliptic curves.
TeX Write-Ups of Sections
Schedule of Final Presentations
Tuesday, May 7 (B129 VV).
9:30 Rachel Davis, "Comparing Constructions (of Universal Deformation Rings)"
9:45 Cathryn Holm, "Not as Easy as ABC!"
10:00 Megan Maguire, "Cohomology of Profinite Groups"
10:15 Carolyn Abbott, "Kummer's Proof of Fermat's Last Theorem for Regular Primes"
10:30 Eric Ramos, "Modularity Lifting Theorems and Serre's Conjecture"
Thursday, May 9 (B129 VV).
9:30 Sara Jensen, "Finite Index Subgroups of Profinite Groups"
9:45 Peng Yu, "Genus and Defining Equations of Modular Curves"
10:00 Serkan Sakar, "Galois Cohomology and its Applications"
10:15 Ahmet Kabakulak, "Fermat's Last Theorem over Other Rings"
10:30 Jonathan Lima, "Modular Forms and Hecke Operators"
Tuesday, May 14 (B223 VV).
2:30 Nathan Clement, "Neron Models: They're Flat out Amazing"
2:45 Yihe Dong, "A Glimpse into Hodge Structures"
3:00 Vlad Matei, "The Faltings-Serre Method"
3:15 Lalit Jain, "Families of Curves with Constant mod N Representations"
3:30 Elaine Brow, "Keeping the Spirit Alive: Fermat-Like Equations"
Thursday, May 16 (B223 VV).
2:30 Vladimir Sotirov, "Galois Groups of p-closed Extensions of p-adic Fields"
2:45 Yueke Hu, "Ribet's Level-Lowering"
3:00 Rohit Nagpal, "Langlands-Tunnell Theorem"
3:15 Jeffrey Poskin,
3:30 Edward Dewey, "Following Your Nose to Schlessinger's Theorem"
Some Final Projects