Research

I study mathematics, specializing in analytic arithmetic geometry. I primarily focus on K-theory, spectral methods, and (∞, n)-categories. I recently introduced the notion of n-rigidity for presentable (∞, n)-categories and am working on constructing an example related to K-theory: noncommutative n-motives.

PhD thesis

In my thesis Berkovich 2-motives and normed ring stacks, I characterize the stable presentable symmetric monoidal (∞, 2)-category of Berkovich 2-motives as freely generated by a ring stack equipped with an absolute value satisfying certain easy-to-verify conditions. A corrected version is available here on arXiv.

Preprints

Certain databases list some preprints as “submitted,” but this is not always accurate. Nevertheless, all these works were written with submission to research journals in mind.

• Inaccessibility of the flat topology.

  Ko Aoki and Robert Burklund.

  [arXiv:2607.09440]

• Berkovich 2-motives and normed ring stacks.

  Ko Aoki.

  [arXiv:2603.01877]

• Higher presentable categories and limits.

  Ko Aoki.

  [arXiv:2510.13503]

• Higher Zariski geometry.

  Ko Aoki, Tobias Barthel, Anish Chedalavada, Tomer Schlank, and Greg Stevenson.

  [arXiv:2508.11621]

• Very Schwartz coidempotents and continuous spectrum.

  Ko Aoki.

  [arXiv:2505.04817]

• Rosenberg’s conjecture for the first negative K-group.

  Ko Aoki.

  [arXiv:2409.09651]

• (Semi)topological K-theory via solidification.

  Ko Aoki.

  [arXiv:2409.01462]

• The smashing spectrum of sheaves.

  Ko Aoki.

  [arXiv:2406.03969]

Peer-reviewed papers

• On cohomology of locally profinite sets.

  Ko Aoki.

  Proc. London Math. Soc. (3) 132 (2026), e70159.

  [arXiv:2411.05995] [doi:10.1112/plms.70159]

• K-theory of rings of continuous functions.

  Ko Aoki.

  Camb. J. Math. 14 (2026), no. 2, 243–283.

  [arXiv:2402.05257] [doi:10.4310/CJM.260514222021]

• The sheaves–spectrum adjunction.

  Ko Aoki.

  To appear in Mathematische Annalen.

  [arXiv:2302.04069]

• Posets for which Verdier duality holds.

  Ko Aoki.

  Selecta Math. (N.S.) 29 (2023), Paper No. 78, 22 pp.

  [arXiv:2202.05312] [doi:10.1007/s00029-023-00887-2]

• Quasiexcellence implies strong generation.

  Ko Aoki.

  J. Reine Angew. Math. 780 (2021), 133–138.

  [arXiv:2009.02013] [doi:10.1515/crelle-2021-0034]

• Tensor triangular geometry of filtered objects and sheaves.

  Ko Aoki.

  Math. Z. 303 (2023), no. 3, Paper No. 62, 27 pp.

  [arXiv:2001.00319] [doi:10.1007/s00209-023-03210-z]

• The weight complex functor is symmetric monoidal.

  Ko Aoki.

  Advances in Mathematics 368 (2020), 107145, 10 pp.

  [arXiv:1904.01384] [doi:10.1016/j.aim.2020.107145]

Talks

A list of research talks is available here.

Reports

• Berkovich 2-motives and normed ring stacks. Extended abstract of my talk at the Oberwolfach workshop on algebraic K-theory, 2025.
• A 2-rigid 2-category of 2-motives. Poster at the BIGS poster exhibition, 2025.
• Presentable (∞, n)-categories. Poster at the BIGS poster exhibition, 2024.
• Analytic K-theory. Poster at the BIGS poster exhibition, 2023.
• Analytic K-theory (progress report). Poster at the BIGS poster exhibition, 2022.