This is the webpage for the section of Undergraduate Seminars I focused on Fermat's last theorem. A tentative syllabus can be found here.
Instructor: Avi Zeff
Time/place: Mondays 1 - 3 PM in 507 Mathematics
Date | Speaker | Topic | Sources | Materials |
September 16 | Avi | Introduction and logistics | ||
September 23 | Leo | Elementary approaches: infinite descent, n = 3, 4, sums of two squares | [H, §1.4 - 1.7] | |
September 23 | Avi | Kummer's approach: proof for regular primes | [H, §1.8] | |
September 30 | Luca | Elliptic functions I | [H, §2.1 - 2.5] | |
September 30 | Shiv | Elliptic functions II | [H, §2.6 - 2.12] | |
October 7 | Avi | Number fields | [H, §3] | |
October 14 | Zach K. | Elliptic curves I: definitions and first properties | [H, §4.1 - 4.5] | |
October 14 | Zachary L. | Elliptic curves II: endomorphisms and bounds | [H, §4.6 - 4.11] | |
October 21 | Kaitlyn | Elliptic curves III: further properties and conjectures | [H, §4.12 - 4.15] | |
October 21 | Zach K. | Modular forms I: theta functions | [H, §5.1 - 5.2] | |
October 28 | Zachary L. | Modular forms II: definitions and first properties | [H, §5.3 - 5.4] | |
October 28 | Shiv | Modular forms III: operations | [H, §5.5 - 5.8] | |
November 11 | Luca | Modularity and Fermat's last theorem I | [H, §5.8 - 6.1] | |
November 11 | Leo | Modularity and Fermat's last theorem II | [H, §6.2 - 6.7] | |
November 18 | Kaitlyn | Addenda and related problems | [H, §6.7 - 6.8] | |
December 2 | Avi | Outline of the proof of modularity | ||
December 9 | Students | Project talks |
[H] Hellegouarch, Yves. Invitation to the mathematics of Fermat–Wiles (Schneps, Leila, Trans.). Elsevier, 2001.