Research

I do research in K-theory, spectral methods, and (∞, n)-categories. Specifically, I study their interactions with functional analysis and general topology.

Reports

• 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.

Preprints

• On cohomology of locally profinite sets.

  Ko Aoki.

  [arXiv:2411.05995]

• 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]

• K-theory of rings of continuous functions.

  Ko Aoki.

  [arXiv:2402.05257]

• The sheaves-spectrum adjunction.

  Ko Aoki.

  [arXiv:2302.04069]

Peer-reviewed papers

• 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]