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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

(Refereed Papers)
  1. N. Ito and Y. Takimura, Knot projections with reductivity two, Topology Appl. 193 (2015), 290—301.
  2. N. Ito and Y. Takimura, Strong and weak (1, 2, 3) homotopies on knot projections, Internat. J. Math. 26 (2015), 1550069 (8 pages).
  3. N. Ito and Y. Takimura, Sub-chord diagrams of knot projections, Houston J. Math. 41 (2015), 701—725.
  4. N. Ito and Y. Takimura, Strong and weak (1, 2) homotopies on knot projections and new invariants, Kobe J. Math., accepted.
  5. N.Ito and Y. Takimura, Triple chords and strong (1, 2) homotopy, J. Math. Soc. Japan, accepted.
  6. 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.
  7. N. Ito, Y. Takimura, and K. Taniyama, "Strong and weak (1, 3) homotopies on knot projections", Osaka J. Math. 52 (2015) 617—647.
  8. N. Ito, “A colored Khovanov bicomplex”, Banach Center Publ. 103 (2014), 111—143.
  9. N. Ito and Y. Takimura, “(1, 2) and weak (1, 3) homotopies on knot projections”, J. Knot Theory Ramifications, 22 (2013), 1350085 (14 pages).
  10. 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.
  11. N. Ito, “Jones polynomials of long virtual knots”, J. Knot Theory Ramifications 22 (2013), 1350002 (17 pages).
  12. N. Ito and A. Shimizu, “The half-twisted splice operation on reduced knot projections”, J. Knot Theory Ramifications 21 (2012), 1250112 (10 pages).
  13. A. Gibson and N. Ito, “Finite type invariants of nanowords and nanophrases”, Topology Appl. 158 (2011), 1050—1072.
  14. N. Ito, “Chain homotopy maps for Khovanov homology”, J. Knot Theory Ramifications 20 (2011), 127—139.
  15. N. Ito, “Construction of invariants of curves and fronts using word theory”, J. Knot Theory Ramifications 19 (2010), 1205—1245.
  16. N. Ito, “Finite-type invariants for curves on surfaces”, Proc. Japan Acad. Ser. A Math. Sci. 85 (2009), 129—134.

(Organized Conference)
  1. Mathematics of Knots Ⅷ, Waseda University, December 2015. Co-organizer: Kouki Taniyama.
  2. WIAS Top Runners’ Lecture Collection of Science “Fluid Dynamics and Geometry” (sponsorship: CREST & WIAS), Waseda University, March 2014.
  3. “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


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