Taketo Sano

My name is Taketo Sano, and I am a mathematician specializing in low-dimensional topology and knot theory. Since 2025, I have been working as a Research Scientist in the Mathematical Application Research Team at RIKEN iTHEMS.

I received my Ph.D. in Mathematical Sciences from the University of Tokyo under the supervision of Prof. Mikio Furuta. Before pursuing graduate studies, I worked as a software engineer in the tech industry from 2007 to 2016. I am also the father of two children—a 10-year-old daughter and a 1-year-old son (as of 2025).

My research focuses on Khovanov homology theory, a knot homology theory introduced by Mikhail Khovanov in 2000 as a categorification of the Jones polynomial. By integrating computational methods into the study of low-dimensional topology, I aim to deepen our understanding of knots and low-dimensional manifolds.

contact: taketo.sano @ riken.jp

Recent Talks

Aug 2025, A diagrammatic approach to Rasmussen invariants.
Extended KOOK Seminar 2025, Osaka Institute of Technology.
[Slides]
Jul 2025, A diagrammatic approach to Rasmussen invariants via tangles and cobordisms.
Tuesday Seminar on Topology, The University of Tokyo.
[Slides]
Nov 2024, Involutive Khovanov homology and equivariant knots.
4 Dimensional Topology 2024 at Osaka U.
[Slides]

Recent Work

Cobordism maps in Khovanov homology and singular instanton homology II, with Hayato Imori, Kouki Sato and Masaki Taniguchi.
In preparation.
Symmetries of equivariant Khovanov homology, with Mikhail Khovanov (2025)
[arXiv]
Cobordism maps in Khovanov homology and singular instanton homology I, with Hayato Imori, Kouki Sato and Masaki Taniguchi (2025)
[arXiv]
A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms, with KeeTaek Kim (2025)
[arXiv / Slides]
More on arXiv.

Publications

An algorithm for computing the Υ-invariant and the d-invariants of Dehn surgeries, with Kouki Sato.
To be published in Quantum Topology.
[DOI / arXiv]
Computations of HOMFLY homology, with Keita Nakagane.
Journal of Knot Theory and Its Ramifications (2025)
[DOI / arXiv]
Involutive Khovanov homology and equivariant knots.
To be published in Algebraic & Geometric Topology.
[DOI / arXiv / Slides]
A family of slice-torus invariants from the divisibility of reduced Lee classes, with Kouki Sato.
Topology and its Applications (2024), Vol. 357, 109059 (2024).
[DOI / arXiv]
A Bar-Natan homotopy type.
International Journal of Mathematics Vol. 34, No. 02, 2350008 (2023).
[DOI / arXiv]
Fixing the functoriality of Khovanov homology: a simple approach.
Journal of Knot Theory and Its Ramifications Vol. 30, No. 11, 2150074 (2021).
[DOI / arXiv]

A description of Rasmussen's invariant from the divisibility of Lee's canonical class.
Journal of Knot Theory and Its Ramifications Vol. 29, No. 06 (2020).
[DOI / arXiv]

My daugther drawing a squid at my research institute.

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