I am a first year graduate student and I am eager to work on irrationality/transcendental proofs of specific numbers like Euler's constant gamma. Because backgrounds for Elliptic Curves include very much of Algebraic Geometry but there is no professor working on Transcendental NT, Analytic NT or Elliptic Curves, so I was wondering is there a subject in the intersection of irrationality/transcendental proofs of specific numbers (or more generally Diophantine approx) with Algebraic Geometry so that I can write a proposal for the professor who works in Algebraic Geometry? I couldn't find any on the Internet.
What are some interesting problems in the intersection of Diophantine Approx and Algebraic Geometry?
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$\begingroup$ The title is helped from mathoverflow.net/questions/103243/… $\endgroup$– user288447Commented Jun 29, 2021 at 12:34
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1$\begingroup$ Do you have an advisor? This is a question more suitable to ask them. $\endgroup$– Stanley Yao XiaoCommented Jun 29, 2021 at 13:05
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1$\begingroup$ Hi L.G! There are many intersections indeed. For instance, the analytic subgroup theorem involves a lot of intricate algebraic geometry and estimates on auxiliary polynomials (see this talk for an introduction: drive.google.com/file/d/1-6j1DPZBMNBS_cOOVcxEHJDGwxhqz7Q6/…). Also, the theory of periods provides a lot of examples of numbers which are conjecturally transcendental (see this book for an introduction: home.mathematik.uni-freiburg.de/arithgeom/preprints/buch-alt/…). $\endgroup$– Riccardo PengoCommented Jun 29, 2021 at 13:49
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2$\begingroup$ Simulposted to m.se, math.stackexchange.com/questions/4186026/… without notice to either site. Don't do that! $\endgroup$– Gerry MyersonCommented Jun 29, 2021 at 13:49
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1$\begingroup$ Gerry wanted to say that you should mention the cross-post on both sides. Don't do that = don't cross-post without notice. $\endgroup$– Z. MCommented Jun 29, 2021 at 14:52
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