# Researchers / Noboru Ito

Noboru Ito

- Doctor of Science
- Associate Professor （without tenure) , Waseda Institute for Advanced Study

## Research Topics

Every finite dimensional vector space has an integer as its dimension. Categorification means some perspective and structure getting more information from vector spaces than that of integers. On the other hand, the set of knots, it often presents that of three dimensional manifolds, is an attractive object appearing in not only Mathematics ---Topology, Algebraic Geometry, Singularity Theory, Fluid Dynamics—but also other areas ---Quantum computing, DNA, human mind, game, etc. This study of mine is trying to attack one of the important mathematical open problem “Categorification of quantum invariants of three dimensional manifolds”. In the process, I am seeking possibilities of applications and collaborations with other areas to support human society.

## Education and Academic Employment

2005.3 | B. Science, Waseda University |

2007.3 | M. Science, Waseda University |

2010.3 | D. Science, Waseda University |

2008.4—2010.3 | JSPS Research Fellow |

2010.4—2011.3 | Research Associate, Dept. of Math., Waseda University |

2011.4—2013.3 | Assistant Professor, Dept. of Math., Waseda University |

2013.4—2015.3 | Assistant Professor, WIAS, Waseda University |

2015.4— | Associate Professor (without tenure), WIAS, Waseda University |

## Research Fields of Interest

- Knots
- Three dimensional manifolds
- Quantum topology
- Geometry

## Academic Publications

- N. Ito and Y. Takimura, Knot projections with reductivity two, Topology Appl. 193 (2015), 290—301.
- N. Ito and Y. Takimura, Strong and weak (1, 2, 3) homotopies on knot projections, Internat. J. Math.
*26*(2015), 1550069 (8 pages). - N. Ito and Y. Takimura, Sub-chord diagrams of knot projections, Houston J. Math.
*41*(2015), 701—725. - N. Ito and Y. Takimura, Strong and weak (1, 2) homotopies on knot projections and new invariants, Kobe J. Math., accepted.
- N.Ito and Y. Takimura, Triple chords and strong (1, 2) homotopy, J. Math. Soc. Japan, accepted.
- K. Hayano and N. Ito, A new aspect of the Arnold invariant J+ from a global viewpoint, Indiana Univ. Math. J.,
*64*(2015), 1343—1357. - N. Ito, Y. Takimura, and K. Taniyama, "Strong and weak (1, 3) homotopies on knot projections", Osaka J. Math.
*52*(2015) 617—647. - N. Ito, “A colored Khovanov bicomplex”, Banach Center Publ.
*103*(2014), 111—143. - N. Ito and Y. Takimura, “(1, 2) and weak (1, 3) homotopies on knot projections”, J. Knot Theory Ramifications,
*22*(2013), 1350085 (14 pages). - N. Ito, “Survey and remarks on Viro’s definition of Khovanov homology”, 9—19, RIMS Kôkyûroku Bessatsu, B39, Res.Inst.Math.Sci.(RIMS), Kyoto, 2013.
- N. Ito, “Jones polynomials of long virtual knots”, J. Knot Theory Ramifications
*22*(2013), 1350002 (17 pages). - N. Ito and A. Shimizu, “The half-twisted splice operation on reduced knot projections”, J. Knot Theory Ramifications
*21*(2012), 1250112 (10 pages). - A. Gibson and N. Ito, “Finite type invariants of nanowords and nanophrases”, Topology Appl.
*158*(2011), 1050—1072. - N. Ito, “Chain homotopy maps for Khovanov homology”, J. Knot Theory Ramifications
*20*(2011), 127—139. - N. Ito, “Construction of invariants of curves and fronts using word theory”, J. Knot Theory Ramifications
*19*(2010), 1205—1245. - N. Ito, “Finite-type invariants for curves on surfaces”, Proc. Japan Acad. Ser. A Math. Sci.
*85*(2009), 129—134.

(Organized Conference)

- Mathematics of Knots Ⅷ, Waseda University, December 2015. Co-organizer: Kouki Taniyama.
- WIAS Top Runners’ Lecture Collection of Science “Fluid Dynamics and Geometry” (sponsorship: CREST & WIAS), Waseda University, March 2014.
- “Quantum invariants of knots and their categorifications”, August 2011, Waseda University. Co-organizer: Kouki Taniyama.

## Other Interests

athletic sports

## Membership of Academic Organization

The Mathematical Society of Japan

## Honors

2005 | Azusa Ono Memorial Scholarship |

2006 | Azusa Ono Memorial Scholarship |

2007 | Grant-in-Aid for young researchers of Waseda University |

2007 | Scholarship of JASSO, Exemption from Repayment recognized by JASSO as having achieved particularly outstanding results during the Master course of study |

2008-2010 | Grant-in-Aid for JSPS Fellows (20・935) |

2010 | Waseda University Grant for Special Research Projects (2010A-863) |

2011-2013 | Grant-in-Aid for Young Scientists (B) of Japan Society for Promotion of Science |

2013 | A candidate for JSPS Postdoctoral Fellow for Research Abroad, 2013 (declined by University’s Rule) |

2015, 3-6 | Invited Visitor, Simons Center for Geometry and Physics |