Niven T. Achenjang

I am a math grad student at MIT, broadly interested in arithmetic geometry and especially in points on varieties. My advisor is Bjorn Poonen.

You can find my cv here, once I make an up to date one.

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news

Oct 12, 2023	I posted a new paper on arxiv. It is about bounding the average size of \(2\)-Selmer groups of elliptic curves \(E\) over characteristic \(2\) function fields. It also produces some new bounds on \(\dim_{\F_2}\Sel_2(E/K)\) when \(\Char K=2\) (and \(K\) is a global function field).
Aug 2023	I’m gonna try running a seminar on modularity and Fermat.
Jul 12, 2023	My paper with Jackson Morrow, in which we construct new examples of irreducible divisors on varieties whose complements can only have finitely many integral points, was published.
Jul 2023	I attended the AGNES Summer School on Intersection Theory on Moduli Spaces.
Jun 2023	I attended an MRC on Explicit Computations with Stacks.

publications

ArXiv

The Average Size of 2-Selmer Groups of Elliptic Curves in Characteristic 2

Achenjang, Niven

2023

arXiv Bib

@misc{achenjang2023average,
  bibtex_show = {true},
  title = {The Average Size of 2-Selmer Groups of Elliptic Curves in Characteristic 2},
  author = {Achenjang, Niven},
  year = {2023},
  month = oct,
  eprint = {2310.08493},
  archiveprefix = {arXiv},
  primaryclass = {math.NT},
  selected = {true},
  arxiv = {2310.08493},
  journal = {arxiv}
}

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

@article{inf-pts-inf-et-fund-gp,
  bibtex_show = {true},
  author = {Achenjang, Niven T and Morrow, Jackson S},
  title = {{Integral Points on Varieties With Infinite Étale Fundamental Group}},
  journal = {International Mathematics Research Notices},
  pages = {rnad147},
  year = {2023},
  month = jul,
  issn = {1073-7928},
  doi = {10.1093/imrn/rnad147},
  url = {https://doi.org/10.1093/imrn/rnad147},
  eprint = {https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnad147/50873758/rnad147.pdf},
  abbr = {IMRN},
  arxiv = {2212.06210},
  html = {http://track.smtpsendmail.com/9032119/c?p=YGn6SveE1TESCW4U4tlsQXeJx04EQHd9FUyu4CwTzsgJO7B4QoSd8_ml2HgN84lanY-URPUmVwWy-5f-6YQpnmBrwb8rnoxyBCh0FuuGQZgZ8kxBy1bbWx4ueP0jF2V6DZQkRvY61zHgLgJePYGDjNIQdKM3k2ipvO5IfHeTlrBSx8fbzkEao2s7gucKcAvzIUYi43AEL1izfpHZKfjcW9Ym3jK39ZTr6pPEivL8FEQ_KpAMASf3yGUv7bTiw_DFzTTeK1jVQN-CFWvWlEFoxLn0senqCBhnOKP5zfkJbvcAjtr_c9AskSFLVwaMTaL6eB_sIqgWCE_nfZthgCu8mg==},
  selected = {true}
}

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

@article{divisor-funcs,
  bibtex_show = {true},
  title = {On gaps in the closures of images of divisor functions},
  author = {Achenjang, Niven and Berger, Aaron},
  year = {2019},
  journal = {International Journal of Number Theory},
  pages = {1023-1036},
  number = {05},
  volume = {15},
  abbr = {IJNT},
  html = {https://www.worldscientific.com/doi/10.1142/S1793042119500556},
  arxiv = {1808.07550},
  selected = {true}
}