London School of Geometry and Number Theory (LSGNT)

Topics in Number Theory


Topics in Number Theory is a semester-and-a-half-long course taught every year to the first-year LSGNT students. This version of the course, on the theme of L-function, is designed by Andrew Granville and Payman Kassaei, and is taught collaboratively by academics in London. Each lecture is followed by a wrap-up session where a student (the owner) presents solutions to exercises and leads discussions. A senior student (the leader) is also present for supervision.

Schedule of lectures

Date

Lecturer

Title

Owner

Leader

Act I: L-functions via counting points

Oct 11 Owen Patashnick Diophantine Equations Angela Wu Gregorio
Oct 18 Alex Betts Counting points on Varieties I: The Chevalley-Warning Theorem Benjamin Aslan Yin
Oct 25 Mahesh Kakde Counting points on Varieties II: Elliptic Curves Matthew Habermann Raffael
Nov 1 Ardavan Afshar Counting points on Varieties III: Diagonal Equations and Jacobi Sums Ashwin Iyengar & Hanneke Wiersema Fabian
Nov 8 Kevin Buzzard L-functions of varieties and the Weil Conjectures Sarah Nowell & Petru Constantinescu Albert
Nov 15 Vladimir Dokchitser L-functions of Elliptic curves: The Birch-Swinnerton-Dyer Conjecture Lorenzo Laporta Giulia

Act II: L-functions via analysis

Nov 22 Igor Wigman The Riemann Zeta function and the Dirichlet L-functions Brad Doyle Andrea
Nov 29 Winston Heap The Analytic Class Number Formula Johannes Girsch Luigi
Dec 6 Payman Kassaei Modular forms and their L-functions I Daniel Platt Galen
Dec 13 James Newton Modular forms and their L-functions II David Sheard Tim

Act III: A unification theory

Jan 17 Kevin Buzzard The Shimura-Taniyama-Weil Conjecture: statement and examples Omri Faraggi & Andrew Graham TBD
Jan 31 fred Diamond A brief survey of the proof of Fermat's Last Theorem I Pol van Hoften & Samuel Stark TBD
Feb 14 Toby Gee A brief survey of the proof of Fermat's Last Theorem II N/A N/A


Times and locations

In Autumn, the lectures take place at room 342, Huxley Building, Imperial College 10-12 am. In Winter, the lectures will be at UCL 10-12 am. The room will be announced later.
The wrap-up session of a lecture is held on the following Tuesday, 10-12 am, Room S4.36, Strand Building, Kings College London.