In Term 1 2016, we are running a study group on the odd Goldbach conjecture (actually a theorem of Vinogradov from 1937, for sufficiently large odd numbers). The goal is to educate ourselves about the ingredients in the proof, and in the process get a general overview of the Hardy--Littlewood circle method and various other techniques in analytic number theory.
Here is the current schedule of speakers:
Introduction/overview of the proof
The Siegel--Walfisz Theorem, part I
The Siegel--Walfisz Theorem, part II
The major arc estimate
Adding up the major arc contributions
The minor arc estimate
Putting everything together/ what would happen in the binary problem?
Extensions (Waring's problem)