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

Apr 2, 2024	I will be travelling to Seattle to talk in UW’s Number Theory Seminar. Exactly what I will talk about is still TBD.
Jan 2024	I gave a talk at JMM this year on my 2-Selmer paper. I will also be talking about it again soon at BU’s Number Theory Seminar on Jan 22. Brown’s Algebra Seminar on Feb 5 Harvard’s Number Theory Seminar on Feb 21.
Nov 29, 2023	Vari ous coau thors and I posted a new paper on arxiv, in which we compute the Brauer group of the moduli stack \(\mathscr Y_0(2)\) parameterizing elliptic curves equipped with a cyclic subgroup of order \(2\).
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.

publications

ArXiv
The Brauer Group of \(\mathscr Y_0(2)\)

Achenjang, Niven, Bhamidipati, Deewang, Jha, Aashraya, Ji, Caleb, and Lopez, Rose

2023

arXiv Bib
@misc{achenjang2023brauer, bibtex_show = {true}, title = {The Brauer Group of \(\mathscr {Y}_0(2)\)}, author = {Achenjang, Niven and Bhamidipati, Deewang and Jha, Aashraya and Ji, Caleb and Lopez, Rose}, year = {2023}, eprint = {2311.18132}, archiveprefix = {arXiv}, primaryclass = {math.AG}, selected = {true}, arxiv = {2311.18132}, journal = {arxiv} }

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}
}