- I was contacted by Giancarlo Urzúa with an intriguing question about configurations of rational curves on elliptic surfaces. We eventually resolved it and found interesting applications: A result on square-freeness of elliptic divisibility sequences over function fields which seems to be much stronger than anything proven before, and an application to geography of surfaces, where we showed the existence of mildly singular surfaces with arbitrary geometric genus, ample canonical class, and with K2 arbitrarily large. (For smooth surfaces, Noether's formula bounds K2 in terms of the geometric genus.) You can read all about in our preprint on the arxiv.
- More recently, we found a strong upper bound on the number of tangencies considered in the paper mentioned just above. The article has just appeared in IMRN. See 2020c on my research page
I have projects for students at several levels. For the last few years, I have enjoyed working with advanced undergraduates on semester-length projects in number theory and related areas. I'd also be happy to talk with graduate students about projects in number theory and algebraic geometry ranging from a quick MS with good prospects for a paper to more substantial PhD projects.
The fastest and most reliable way to reach me is via e-mail at firstname.lastname@example.org. To make an appointment, please contact my colleagues Alejandra (Ali) Gaona (520-621-2868, email@example.com) or Aubrey Mouradian (520-621-2713, firstname.lastname@example.org).
My short CV.
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