By "advanced number theory", I mean topics like arithmetic/Diophantine geometry, modular/automorphic forms and Shimura varieties. I'm interested in derived/non-commutative algebraic geometry, some topology and higher category theory as well as string theory related things. According to a professor teaching my K-theory class, I only have to know (for topology) elliptic curves and algebraic number theory, both of which I have learned but nothing beyond them. However, as I'm trying to learn topics like geometric Langlands, which are closely related to modular/automorphic forms and other number theory topics, I've been increasingly aware of the influence of number theory in my field.

  • $\begingroup$ so a geometer is a researcher in pure maths ? hence I guess it depends highly on your precise PhD subject. $\endgroup$ – reuns Feb 13 '16 at 4:19
  • $\begingroup$ Yes. My PhD subject is non-commutative algebraic geometry, but the field of my interest is rather broader than that. So, I wanted recommendation for general geometers, but then it may be too broad for any suggestion. If my question is not well-posed and therefore doesn't get any answer, I will close it and post a question by trying to make it more well-posed. $\endgroup$ – Math.StackExchange Feb 13 '16 at 4:41

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