Here is a growing list of resources! Some I know well, some I want to know well - if you think there is anything glaring missing do let me know! You can search using the box below, each entry has a (hidden) list of searchable tags attached to it. Try searching "Shimura curves" for example!

Books

  • Algebraic Number Theory

  • Fourier Analysis on Number Fields by Ramakrishnan and Valenza.
  • Euler Systems by Karl Rubin.

  • Automorphic Forms and Representations

  • Bump - Automorphic Forms and Representations
  • Gelbart - Automorphic Forms on Adele Groups
  • Getz-Hahn "Introduction to Automorphic Representations"
  • Both books by Goldfeld and Hundley on the automorphic representations of GL(n).
  • The Corvallis proceedings, Volume 1 and Volume 2

  • Elliptic Curves

  • Diamond, Shurman

Other Mathematicians Pages

Seminars

Online Notes

  • Algebraic Number Theory

  • Mazur's introductory lecture on Euler systems.
  • Kolyvagin Systems by Mazur and Rubin.
  • Notes on Euler systems and Kolyvagin systems by Rubin.

  • Arithmetic Geometry

  • Notes by Corwin on the Chabauty-Kim method.
  • Notes by Dore on monomdromy in arithmetic geometry.
  • An overview of Lawrence-Venkatesh's proof of the Mordell conjecture.
  • Poonen's notes on p-adic approaches to rational points.

  • Automorphic Forms and Representation

  • Cogdell's notes on automorphic L-functions
  • Sarnak's notes on the generalised Ramanujan conjecture from the CMI proceedings on Trace Formulae, Motives and Shimura Varieties.

  • Class Field Theory

  • An interesting paper by Wyman on reciprocity laws.

  • Combinatorics

  • Ram Murty's overview of Ramanujan graphs.

  • Galois Representations

  • Ribet wrote a review article on Galois representations and Fermat's Last Theorem.

  • Motives

  • Elliott's notes on Motives and Motivic L-functions

  • p-adic Hodge Theory

  • The canonical set of notes on p-adic Hodge theory by Brinon and Conrad.
  • A review of p-adic Hodge theory by Nizioł.

  • p-adic L-functions

  • An overview of p-adic L-functions and trivial zeros by Perrin-Riou.

  • Representation Theory

  • Matt Kerr's notes on the representation theory of SL2(R).

  • Shimura Varieties

  • Notes by Michael Harris on automorphic Galois representations and cohomology of Shimura varieties.
  • Shou-Wu Zhang's notes on Shimura curves.