I am currently looking for a Masters thesis subject in number theory. My favourite subjects are algebraic number theory and cohomologies (I only studied De Rham cohomology).

I've been lately reading some papers around classical BSD and p-adic analogue (conjecture based on Tate–Shafarevich group), Selmer groups, Goldfeld's conjecture... before I actually study elliptic curves and modular forms but I have few notions.

So far, I am not being able to identify a subject around BSD. My approach have been reading papers, and see if there is a need to generalize to a wider range of objects, or maybe the opposite way, try to apply a general theorem to specific type of curves. I think my failure is expectable: I am new to the subject and I don't know what's really the purpose of a Masters thesis? Find something new or rather study the state of the art of a known problem.

Could anyone help me? advices, references are more than welcome.

P.S.: W.Stein's blog suggests few topics but even him is not sure whether those are unsolved problems. I don't know which topics might be feasible in the time span of a Masters thesis.

Thank you for your help.


closed as off-topic by rschwieb, Will Jagy, KReiser, Klaus, Shogun Aug 7 at 16:10

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Seeking personal advice. Questions about choosing a course, academic program, career path, etc. are off-topic. Such questions should be directed to those employed by the institution in question, or other qualified individuals who know your specific circumstances." – rschwieb, Will Jagy, KReiser, Klaus, Shogun
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 3
    $\begingroup$ Defining the relevant objects for the BSD conjecture, Galois representations and the modularity theorem is already a master thesis in itself $\endgroup$ – reuns Aug 6 at 1:56
  • $\begingroup$ @reuns Thank you for your reply and the sample masters thesis $\endgroup$ – PerelMan Aug 6 at 2:14
  • 1
    $\begingroup$ I'm not sure this site is appropriate for soliciting specific ideas for theses. Moreover, the expectations for Master's theses vary with location, department and advisor. $\endgroup$ – Kimball Aug 6 at 5:21