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I am highly interested in doing research in either of

1- Transcendental Number Theory and Algebraic Independence;

2- Diophantine Approximation and Geometry of Numbers.

There is no person working on these areas in the university that I want to study MSc. So I have to choose a "closer" research area for MSc so that I can switch the subject to work on the mentioned primary research interests of mine for PhD.

The reason that I am asking this from this community is because I can't get advice from the faculty: I need to choose the area of research before meeting the would-be supervisor because I want to be prepared by reading some of his/her papers beforehand (like preparing for an interview) to get a chance of admission...

The list of areas of research in the department are:

1- Analytic Number Theory, Additive Problems in Number Theory, Sparse Sequences, Exponential/Character Sums, Automorphic Forms and L-Functions, Density Theorems;

2- Algebraic Number Theory, Elliptic Curves, Complex Multiplication,The Class Numbers of Ray Class Fields of Imaginary Quadratic Fields, Arithmetically Exceptional Mappings;

3- Functional Analysis.

Which area of research is the closest to 1- Transcendental Number Theory and Algebraic Independence, or/and Diophantine Approximation and Geometry of Numbers?

Thank you!

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  • $\begingroup$ I'm not an expert in either the field you're interested in, or the ones you mention, but isn't Analytic Number Theory the closest one ? Or perhaps something related to Galois theory, so the one with "ring theory", "invariant theory" and "cohomology of groups" may be suited as well, depending on the specific courses they offer $\endgroup$
    – Maxime Ramzi
    Commented Feb 13, 2019 at 11:17
  • $\begingroup$ You really should talk to actual faculty in the actual department that you are going to attend. The individual professor's interests and knowledge are certainly going to be more nuanced than any attempt at classification of different areas of mathematics. You can ask to talk to them even before you are admitted. Failing that, at least look at their papers to see how interested you are in what they do. $\endgroup$
    – Boris Bukh
    Commented Feb 28, 2019 at 14:04

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You might find it inspiring/instructive to read this survey of the connections between Diophantine Approximation, on the one hand, and Analytic Number Theory, on the other hand. As you can read, there was at least one researcher who throughout his career worked very fruitfully in both these fields of number theory.

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