$$ \DeclareMathAlphabet{\matheuler}{U}{eus}{m}{n} \newcommand\F{\mathbb F} \newcommand\P{\mathbb P} \newcommand\A{\mathbb A} \newcommand\T{\mathbb T} \newcommand\msO{\mathscr O} \newcommand\msL{\mathscr L} \newcommand\ms{\mathscr} \newcommand\GL{\opname{GL}} \newcommand\eps{\varepsilon} \newcommand\opname{\operatorname} \newcommand\Proj{\opname{Proj}} \newcommand\Pic{\opname{Pic}} \newcommand\hom{\opname H} \newcommand\Char{\opname{char}} \newcommand\Hom{\opname{Hom}} \newcommand\Sel{\opname{Sel}} \newcommand\inv[2][1]{#2^{-#1}} \newcommand\pinv[2][1]{\inv[#1]{\p{#2}}} \newcommand\p[1]{\left(#1\right)} $$

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. Recently, I have most actively been thinking about Brauer groups of stacky curves, but I have also studied some “bad characteristic” statistics of ranks of elliptic curves and have some finiteness results for integral points on high dimensional varieites.

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

I am currently on the job market and am very happy to come talk about my work!

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There are many hidden secrets on this site. Try and find them all (seems some of them are less hidden on mobile...).

news

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.
Apr 2, 2024 I will be travelling to Seattle to talk in UW’s Number Theory Seminar on work which appeared in my Brauer paper with Deewang, Aash, Caleb, and Rose.

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