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Niven T. Achenjang

Welcome!

I am a math grad student at MIT working with Bjorn Poonen and broadly interested in arithmetic geometry and especially in points on varieties. I generally like applying algebro-geometric arguments and cohomology computations in the service of proving finiteness results. I have work on Brauer groups of stacky curves, “bad characteristic” statistics of ranks of elliptic curves, and integral points on high dimensional varieties.

You can find more information about my research in my cv or under the “news” header below.

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news

Apr 2025 I am giving my thesis defense on April 15th. If I know you personally but forgot to mention this to you, you’re interested in attending, and you’re looking at my website for some reason, send me message and I’ll send you the room number and/or zoom link.
Nov 3, 2024 I will be in the Netherlands, in Groningen, from November 3 – 9 for the Instructional workshop on rational points.
Oct 2024 I spoke at the Québec-Maine Number Theory Conference on my recent work on Brauer groups of stacky curves. Later that week, I posted the paper containing this work to arxiv. Later in the month, I spoke about it again at the AMS’s Fall Western Sectional Meeting at UC Riverside and then at Rice’s algebraic geometry and number theory seminar.
Sep 4, 2024 I attended Oberwolfach’s Explicit Methods in Number Theory workshop, where I gave a talk about some of my recent, ongoing work computing Brauer groups of stacky curves. In particular, I discussed a computation of the Brauer group of a tame stacky curve over an algebraically closed field (unlike in the scheme case, these are often nonzero).
Jul 9, 2024 I gave a lightning talk at MIT’s Mordell conjecture conference on my 2-Selmer work.
Jun 2, 2024 I spoke at GTA: Philadelphia on mine and Jackson Morrow’s paper constructing irreducible divisors \(D\) for which we can prove finiteness of \(D\)-integral points.

publications

  1. ArXiv
    On Brauer groups of tame stacks
    Achenjang, Niven
    2024
    arXiv Bib
  2. ArXiv
    The Brauer Group of \(\mathscr Y_0(2)\)
    Achenjang, Niven, Bhamidipati, Deewang, Jha, Aashraya, Ji, Caleb, and Lopez, Rose
    2023
    arXiv Bib
  3. ArXiv
    The Average Size of 2-Selmer Groups of Elliptic Curves in Characteristic 2
    Achenjang, Niven
    2023
    arXiv Bib
  4. IMRN
    Integral Points on Varieties With Infinite Étale Fundamental Group
    Achenjang, Niven T, and Morrow, Jackson S
    International Mathematics Research Notices,  2023
    JOURNAL arXiv Bib
  5. IJNT
    On gaps in the closures of images of divisor functions
    Achenjang, Niven, and Berger, Aaron
    International Journal of Number Theory,  2019
    JOURNAL arXiv Bib