Taketo Sano

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

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

Since the beginning of my research career, I have been focusing on Khovanov homology theory, introduced by M. 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 Works

A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms.
[arXiv]
Involutive Khovanov homology and equivariant knots.
To be published in Algebraic & Geometric Topology.
[arXiv / Slides]
More on arXiv.

Publications

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]

Recent Talks

Nov 2024, Involutive Khovanov homology and equivariant knots.
4 Dimensional Topology 2024 at Osaka U.
[Slides]
July 2024, Khovanov homology and its applications to low-dimensional topology.
3-days lectures at KAIST, Korea.
[Notes]

June 2024, Khovanov homology and its applications to low-dimensional topology.
3-days lectures at OIST, Japan.
[Link]

Teaching

Introduction to Morse Theory, Gakushuin University, 2024.
General Topology, Kokushikan University, 2023.
Calculus and Linear Algebra, Komazawa University, 2022.

My daugther drawing a squid at my research institute.

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