Most recently, I was a senior research fellow at University College London, and before that I was a member of the Institute for Advanced Study in Princeton. I have a PhD from Imperial College London and undergraduate degrees from the University of Oxford. If you would like to contact me, my email is bodan.arsovski@outlook.com.

Selected writings

Not everything I have written is on the arXiv, and in some cases there are significant differences between the published version and the arXiv version, an unfortunate necessity for copyright reasons.

  • Work on the Kakeya conjecture: J. Amer. Math. Soc. 37, 69–80
    The classical Kakeya conjecture states that all compact subsets of ℝ𝑛 containing a line segment of unit length in every direction have full Hausdorff dimension. In this article I prove the natural analogue of the classical Kakeya conjecture over the 𝑝-adic numbers β€” more specifically, that all compact subsets of β„šπ‘›π‘ containing a line segment of unit length in every direction have full Hausdorff dimension β€” a conjecture which was first discussed in the 1990s by James Wright. In fact, more generally I prove the 𝑝-adic analogue of the Kakeya maximal conjecture, which is a functional version of the Kakeya conjecture proposed by Jean Bourgain in the 1990s. The reason this is interesting is that the Kakeya conjecture boils down to the highly combinatorial question of packing thin tubes as tightly as possible, and in all known cases (such as 𝑛=2, where the optimal packing volume is precisely known) tubes can be packed exactly as tightly in β„šπ‘›π‘ as in ℝ𝑛. This result was mentioned in Quanta Magazine in the articles β€œA question about a rotating line helps reveal what makes real numbers special” and β€œThe year in math”.
  • Work on representation theory: Res. Math. Sci. 8, #12, Doc. Math. 26, 1929–1979, pdf, pdf, pdf
    This sequence makes up the math I worked on for my PhD thesis.
  • Work on Snevily’s conjecture: Israel J. Math. 182, 505–508
    Here I prove a conjecture that is the subject of section 9.3 of this book by Terence Tao and Van Vu.

Selected teaching

In 2025, I taught a problem class in MATH0014 (Further Linear Algebra) to second year undergraduates at UCL, and also covered lectures in MATH0008 (Applied Mathematics) for first year undergraduates at UCL.