I am Bodan Arsovski, currently a senior research fellow at University College London, part of the University of London. Previously, I was briefly a postdoc at the Institute for Advanced Study in Princeton, New Jersey (for 11 months) and the University of Sheffield (for 3 months), and I graduated from Imperial College London (PhD) and the University of Oxford (MMath and BSc). Check out my cv for more details and my contact info.

Publications

This is the most up to date list of my publications and preprints. In particular, not all of them are on the arXiv, and in some cases there is a significant difference between the published version and the arXiv version, an unfortunate necessity for copyright reasons.

  1. “The p-adic 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 — more specifically, that all compact subsets of ℚ𝑛𝑝 containing a line segment of unit length in every direction have full Hausdorff dimension — 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 ℚ𝑛𝑝 as in ℝ𝑛. This result was mentioned in Quanta Magazine in the articles “A question about a rotating line helps reveal what makes real numbers special” and “The year in math”.
  2. “On the Minkowski dimension of certain Kakeya sets” Mat. Bilten 46, 77–82
  3. “Limiting measures of supersingularities” latest preprint
  4. “On the reductions of certain 2D crystalline representations, III” latest preprint
  5. “On the reductions of certain 2D crystalline representations, II” latest preprint
  6. “On the reductions of certain 2D crystalline representations” Doc. Math. 26, 1929–1979
  7. “On the reductions of certain 2D crystabelline representations” Res. Math. Sci. 8, #12
    Articles 3–7 make up the math I worked on for my PhD thesis. In summary: I make progress toward a conjecture by Fernando Gouvêa from 2001. I prove a special case of a conjecture by Breuil&Buzzard&Emerton from 2005. And, I disprove a conjecture by Buzzard&Gee from 2015, and classify all small counterexamples. Plus, there are a bunch of nice computations of representations associated with modular forms.
  8. “Additive bases via Fourier analysis” Combin. Probab. Comput. 30, 930–941
  9. “A proof of Snevily’s conjecture” Israel J. Math. 182, 505–508
    In this article I prove a conjecture by Hunter Snevily. Snevily’s conjecture comprises section 9.3 of the book “Additive Combinatorics” by Terence Tao and Van Vu. At the time, the conjecture was 10 years old, and partial results had been obtained by Noga Alon and Dasgupta&Károlyi&Serra&Szegedy. Recorded talk at the Isaac Newton Institute for Mathematical Sciences.

Teaching

In 2025, I taught a problem class in MATH0014 (Further Linear Algebra) to second year undergraduates at UCL. These were classes in a typical classroom setting, for an audience of ≈20. I also covered lectures in MATH0008 (Applied Mathematics) for first year undergraduates at UCL. These were lectures in a lecture hall setting, for an audience of ≈200. In 2026, I will be teaching tutorials in MATH0011 (Mathematical Methods), which is a broad introductory course for first year undergraduates at UCL. I have also given invited lectures at various conferences, e.g., at the Isaac Newton Institute for Mathematical Sciences, the Institute for Advanced Study, UCLA, the University of Edinburgh, etc.