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.

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news

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.
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. One aesthetically pleasing consequence of this work is that it completes the proof that the average rank of elliptic curves over \(K\) is finite, for any global field \(K\).

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}
}