ITO Noboru

J-GLOBAL         Last updated: Nov 16, 2019 at 06:36
 
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Name
ITO Noboru
URL
http://www.ms.u-tokyo.ac.jp/~noboru/index.html
Affiliation
The University of Tokyo
Section
Graduate School of Mathematical Sciences

Research Areas

 
 

Books etc

 
伊藤 昇
日本評論社   Mar 2018   ISBN:4535788138
伊藤 昇(数学)
CRC Press   2016   ISBN:9781498736756

Academic & Professional Experience

 
Apr 2016
 - 
Mar 2017
Project Researcher, Graduate School of Mathematical Sciences, The University of Tokyo
 
Apr 2015
   
 
-- Associate Professor (Fixed Term)
 
 
 - 
Mar 2015
2013.4--2015.3 Assistant Professor, Waseda Institute for Advanced Study
 
 
 - 
Mar 2013
2011.4--2013.3 Assistant Professor, Department of Mathematics, Waseda University
 
 
 - 
Mar 2011
2010.4--2011.3 Research Associate, Department of Mathematics, Waseda University
 
 
 - 
Mar 2010
2008.4--2010.3 JSPS Research Fellow
 

Published Papers

 
Space of chord diagrams on spherical curves
Noboru Ito
Internat. J. Math.   Online Ready 1950060-1-1950060-25   Aug 2019   [Refereed]
RII number of knot projections
Noboru Ito, Yusuke Takimura
Kobe. J. Math.   accepted (2019/08/01)    Aug 2019   [Refereed]
Higher-order finite type invariants of classical and virtual knots and unknotting operations
Noboru Ito, Migiwa Sakurai
Topology Appl.   264 210-222   Jun 2019   [Refereed][Invited]
Noboru Ito, Migiwa Sakurai
J. Math. Soc. Japan   71(1) 329-347   Nov 2018   [Refereed]
Noboru Ito, Yusuke Takimura
Internat. J. Math.   29(12)    Oct 2018   [Refereed]
The tabulation of prime knot projections with their mirror images up to eight double points
Noboru Ito, Yusuke Takimura
Topology Proc.   53 177-199   Oct 2018   [Refereed]
Yukari Funakoshi, Megumi Hashizume, Noboru Ito, Tsuyoshi Kobayashi, Hiroko Murai
J. Knot Theory Ramifications   27(12)    Oct 2018   [Refereed]
Noboru Ito
Kodai Math. J.   41(2) 375-396   Jun 2018   [Refereed]
伊藤 昇
日本物理学会誌 = Butsuri   73(2) 76-84   Feb 2018   [Refereed][Invited]
Circle arrangements of link projections
Noboru Ito, Shosaku Matsuzaki, Kouki Taniyama
Kobe J. Math.   34 27-36   Dec 2017   [Refereed]
Noboru Ito, Yusuke Takimura
Topology Appl.   225 130-138   Jul 2017   [Refereed]
Noboru Ito, Yusuke Takimura
Topology Appl.   210 22-28   Sep 2016   [Refereed]
Noboru Ito, Yusuke Takimura
J. Math. Soc. Japan   68(2) 637-651   Apr 2016   [Refereed]
Strong and weak (1, 2) homotopies on knot projections and new invariants
Noboru Ito, Yusuke Takimura
Kobe J. Math.   33 13-30   2016   [Refereed]
Kenta Hayano, Noboru Ito
Indiana Univ. Math. J.   64(5) 1343-1357   Nov 2015   [Refereed]
Noboru Ito, Yusuke Takimura
Topology Appl.   193 290-301   Sep 2015   [Refereed]
Noboru Ito, Yusuke Takimura
Internat. J. Math.   26(9)    Aug 2015   [Refereed]
Noboru Ito, Yusuke Takimura, Kouki Taniyama
Osaka Journal of Mathematics   52(3) 617-646   Jul 2015   [Refereed]
Sub-chord diagrams of knot projections
Noboru Ito, Yusuke Takimura
Houston J. Math.   41(2) 701-725   Jun 2015   [Refereed]
A colored Khovanov bicomplex
Noboru Ito
Banach Center Publications   103 111-143   Jan 2015   [Refereed]
Noboru Ito, Yusuke Takimura
J. Knot Theory Ramifications   23(8)    Jul 2014   [Refereed]
Noboru Ito, Yusuke Takimura
J. Knot Theory Ramifications   22(14) 1350085   Dec 2013   [Refereed]
Survey and remarks on Viro's definition of Khovanov homology
Noboru Ito
RIMS Kôkyûroku Bessatsu   B39 9-19   Apr 2013   [Refereed]
Noboru Ito
J. Knot Theory Ramifications   22(2)    Feb 2013   [Refereed]
Noboru Ito, Ayaka Shimizu
J. Knot Theory Ramifications   21(11)    Oct 2012   [Refereed]
Andrew Gibson, Noboru Ito
Topology Appl.   158(8) 1050-1072   May 2011   [Refereed]
Noboru Ito
J. Knot Theory Ramifications   20(1) 127-139   Jan 2011   [Refereed]
Noboru Ito
J. Knot Theory Ramifications   19(9) 1205-1245   Sep 2010   [Refereed]
Noboru Ito
Proc. Japan Acad. Ser. A Math. Sci.   85(9) 129-134   Nov 2009   [Refereed]

Others (submitted preprints)

 
Nov 2019   Crossing change on Khovanov homology and a categorified Vassiliev skein relation (with Jun Yoshida)
In this paper, we obtain a categorified version of Vassiliev skein relation on Khovanov homology. More precisely, we will show that the genus-one operation (on TQFT) gives rise to a crossing change on Khovanov complexes. Invariance under Reidemeister moves turns out, and it enables us to extend Khovanov homology to singular links. We then see that its long exact sequence categorifies Vassiliev skein relation for the Jones polynomials. We also discuss the FI relation.
Sep 2019   Toward topological consideration of bipartite networks
May 2019   On a Poincare polynomial from Khovanov homology and Vassiliev invariants (with M. Kameyama)
Apr 2019   Crosscap number of knots and volume bounds (with Y. Takimura)
Apr 2019   Positive knots and weak (1, 3) homotopy (with Y. Takimura)
Mar 2019   A lower bound of crosscap numbers of alternating knots (with Y. Takimura)
Dec 2018   On Goussarov-Polyak-Viro conjecture of knots with degree three (with Y.Kotorii)
Dec 2018   New deformations on spherical curves and Oestlund conjecture (with M. Hashizume)
Nov 2018   On Khovanov complexes
Oct 2018   Crosscap number three alternating knots (with Y. Takimura)
May 2018   Arrow diagrams on spherical curves and actual computations (with M. Takamura)
Nov 2015   Any nontrivial knot projections with no triple chords has a monogon or a bigon (with Y. Takimura)

Misc

 
An introduction to Khovanov homology and an R-matrix
ITO Noboru
12-21   Mar 2017
伊藤 昇, 瀧村 祐介, 谷山 公規
数理解析研究所講究録   1960 101-106   Aug 2015   [Invited]

Research Grants & Projects

 
Categorifications of quantum invariants of knots, Study of spherical curves

Social Contribution

 
[Planner, Organizing Member]  22 Aug 2018 - 24 Aug 2018
Contribution to KnotInfo
[Others]  KnotInfo: https://www.indiana.edu/~knotinfo/descriptions/td_clasp_number.html  2018 - 2018

Conference Activities & Talks

 
On crosscap numbers of knots [Invited]
ITO Noboru
The Third Pan-Pacific International Conference on Topology and Applications   9 Nov 2019   
On the existence of a colored Khovanov bicomplex [Invited]
ITO Noboru
Representation Theory and its Combinatorial Aspects   31 Oct 2019   
Extending Khovanov homology to singular knots based on Vassiliev skein relation (with J.Yoshida)
ITO Noboru
Kohno Lab. Intensive Seminar 2019   26 Sep 2019   Toshitake Kohno
In the definition of Khovanov homology, the skein relation of Kauffman bracket is categorified by the mapping cone corresponding to a saddle of (1+1) TQFT. In this talk, using a correspondence between a canonical short exact sequence of another m...
Crosscap numbers and volume bounds [Invited]
ITO Noboru
Gokayama Topology ・Geometry Seminar 2019   31 Aug 2019   
Crosscap numbers and volume bounds [Invited]
ITO Noboru
23 Jun 2019   
Chain homotopy maps for Khovanov homology [Invited]
ITO Noboru
23 Jun 2019   
Crosscap numbers and volume bounds
ITO Noboru
22 Mar 2019   
Crosscap number two alternating knots
ITO Noboru
19 Mar 2019   
On the degree three case of Goussarov-Polyak-Viro Conjecture of knots
ITO Noboru
19 Mar 2019   
Crosscap number two alternating knots and Kauffman states [Invited]
ITO Noboru
12 Feb 2019   
On crosscap number two alternating knots
ITO Noboru
23 Dec 2018   
Introduction to Khovanov homology and Milnor conjecture [Invited]
ITO Noboru
14 Nov 2018   
Goussarov-Polyak-Viro conjecture of knots with degree three and reduced Polyak algebra
ITO Noboru
18 Sep 2018   
Finite type invariants and n-similarity of virtual knots by forbidden moves
ITO Noboru, SAKURAI Migiwa
20 Mar 2018   
On equivalence classes of spherical curves by deformations of type RI and RIII
ITO Noboru, HASHIZUME Megumi
20 Mar 2018   
Crosscap number two alternating knots
9 Mar 2018   
Spaces of chord diagrams of spherical curves
ITO Noboru
25 Dec 2017   
Crosscaps and knot projections [Invited]
ITO Noboru
23 Oct 2017   
Crosscaps and knot projections [Invited]
ITO Noboru
25 Sep 2017   
On n-trivialities of classical and virtual knots for some unknotting operations
ITO Noboru, SAKURAI Migiwa
13 Sep 2017   
Spaces of chord diagrams of spherical curves [Invited]
ITO Noboru
6 Sep 2017   
An introduction to finite type invariants of knots [Invited]
ITO Noboru
5 Sep 2017   
Spaces of chord diagrams on spherical curves II
ITO Noboru
26 Mar 2017   
Strong and weak (1, 3) homotopies on knot projections
ITO Noboru
12th East Asia School of Knots and Related Topics   13 Feb 2017   
Any nontrivial knot projection with no triple chords has a monogon or a bigon
ITO Noboru
21 Dec 2016   
An introduction to Khovanov homology and an R-matrix [Invited]
ITO Noboru
17 Dec 2016   
A survey of Khovanov homology and a genus bound [Invited]
ITO Noboru
7 Nov 2016   
A new aspect of the Arnold invariant J+ from a global viewpoint [Invited]
ITO Noboru
17 Oct 2016   
Spaces of chord diagrams on spherical curves I
ITO Noboru
18 Sep 2016   
Any nontrivial knot projection with no triple chords has a monogon or bigon
ITO Noboru, TAKIMURA Yusuke
18 Sep 2016   
Spaces of chord diagrams of spherical curves [Invited]
ITO Noboru
Tuesday Seminar on Topology,東京大学   21 Jun 2016   
Triply graded knot projections under (1, 3) homotopy
ITO Noboru, TAKIMURA Yusuke
16 Mar 2016   
Thirty-two equivalence relations on knot projections
ITO Noboru, Takimura Yusuke
16 Mar 2016   
Knot projections with reductiveity two
ITO Noboru
24 Dec 2015   
Triply graded knot projections under (1, 3) homotopy [Invited]
ITO Noboru
18 Dec 2015   
Triple chords and knot projections
ITO Noboru
24 Oct 2015   
Based chord diagrams for spherical curves
ITO Noboru
13 Sep 2015   
Strong and weak (1, 2, 3) homotopies on knot projections
ITO Noboru, TAKIMURA Yusuke
13 Sep 2015   
Introduction to spaces of chord diagrams of the set of the spherical curves [Invited]
ITO Noboru
19 Jul 2015   
Strong and weak (1, 3) homotopies on spherical curves and related topics [Invited]
ITO Noboru
22 May 2015   
Sub-chord diagrams of knot projections
ITO Noboru, TAKIMURA Yusuke
24 Mar 2015   
Circle arrangements on spherical curves
ITO Noboru
24 Mar 2015   
Strong and weak (1, 3) homotopies on knot projections
ITO Noboru
Knot Theory and Its Applications to Physics and Quantum Computing,UT Dallas, in honor of work of Prof. J. H. Przytycki on his 60th birthday   8 Jan 2015   
Classification problems of spherical curves under restricted Reidemeister moves
Shinto Topology Seminar   2015   
Triple chords and strong (1, 2) homotopy
ITO Noboru
25 Dec 2014   
Strong and weak (1, 3) homotopy equivalence classes of spherical curves [Invited]
ITO Noboru
18 Nov 2014   
A new aspect of the Arnold invariant J+ from a global viewpoint
ITO Noboru
27 Sep 2014   
Strong and weak (1, 2) homotopies on spherical curves and new invariants
ITO Noboru
27 Sep 2014   
Triple chords and strong (1, 2) homotopy
ITO Noboru
27 Sep 2014   
Maps on Khovanov chain groups [Invited]
ITO Noboru
4 Jul 2014   
Definitions of Khovanov homology and colored Jones homology [Invited]
ITO Noboru
4 Jul 2014   
Strong (1, 3) homotopy equivalence class containing the trivial circle [Invited]
ITO Noboru
10 May 2014   
Introduction to weak and strong (1, 3) homotopies on spherical curves [Invited]
ITO Noboru
25 Apr 2014   
Strong and weak (1,3) homotopies on knot projections,
ITO Noboru, TAKIMURA Yusuke, TANIYAMA Kouki
15 Mar 2014   
(1,2) homotopies on knot projections
ITO Noboru
15 Mar 2014   
A Khovanov bicomplex [Invited]
ITO Noboru
The Algebra & Geometry of Modern Physics, University of Warsaw   23 Jan 2014   
Knots and me
The 60th Monthly Workshop   2014   
Open problems on knots, curves, and wave fronts
Fluid and Geometry (Waseda University)   2014   
(1, 2) homotopy on knot projections
ITO Noboru
20 Dec 2013   
Some equivalence relations on knot projections
ITO Noboru
5 Oct 2013   
(1, 2), weak (1, 3), and strong (1, 3) homotopies on knot projections [Invited]
ITO Noboru
4 Oct 2013   
Introduction to Khovanov bicomplex [Invited]
ITO Noboru
30 Sep 2013   
Behaviors of Khovanov homology under Kirby moves [Invited]
ITO Noboru
International Conference on Topology and Geometry 2013,Shimane University   2 Sep 2013   
A case study on WRT invariant and Khovanov homology [Invited]
ITO Noboru
Special Topology Seminar,The George Washington University   10 May 2013   
A case of the WRT invariant and Khovanov homology [Invited]
ITO Noboru
Knots in Washington XXXVI,The George Washington University   3 May 2013   
Introduction to non-triviality of Gauss words [Invited]
ITO Noboru
The Discrete Mathematics Seminar,University of South Florida   12 Feb 2013   
Introduction to non-triviality of Gauss words (Joint work with Andrew Gibson)
The Discrete Mathematics Seminar   2013   
Introduction to Khovanov homology I, II, and III
Discussions on Categorifications   2013   
Introduction to Khovanov homology and Kirby moves [Invited]
ITO Noboru
Topology Seminar, Department of Mathematics, The George Washington University   11 Dec 2012   
Khovanov homology and Kirby moves [Invited]
ITO Noboru
Knots in Washington XXXV (The George Washington University),The George Washington University   9 Dec 2012   
Invariants of curves on surfaces and knot invariants [Invited]
ITO Noboru
1 Sep 2012   
On Khovanov bicomplex and related problems [Invited]
ITO Noboru
Topology Seminar, Department of Mathematics, The George Washington University   2 May 2012   
Half-twisted splice on reduced knot projections [Invited]
ITO Noboru
Topology Seminar, Department of Mathematics, University of California   13 Mar 2012   
Invariants of curves on surfaces and knot invariants (Joint work with Andrew Gibson)
Topological Studies around Riemann Surfaces   2012   
Chain homotopy maps for Khovanov homology and finite type invariants of nanophrases [Invited]
ITO Noboru
13 Nov 2011   
Chain homotopy maps for Khovanov homology and finite type invariants of nanophrases [Invited]
ITO Noboru
11 Nov 2011   
Remarks on nanophrases and Jones polynomials
ITO Noboru
15 Oct 2011   
Khovanov homology for an unnormalized Witten-Reshetikhin-Turaev invariant [Invited]
ITO Noboru
11 Aug 2011   
Khovanov homology for an unnormalized Witten-Reshetikhin-Turaev invariant and 3-manifolds
ITO Noboru
Geometry of Transformation Groups and Combinatorics, RIMS Kyoto University   13 Jun 2011   
A relation between Khovanov homology and Kirby moves [Invited]
ITO Noboru
Knots in Washington XXXII, The George Washington University   30 Apr 2011   
On some Khovanov homologies for links in I-bundles and nanophrases
ITO Noboru
20 Mar 2011   
Versions of Jones polynomial [Invited]
ITO Noboru
Darmstadt-Tokyo Spring School: Mathematical Fluid Dynamics, TU Darmstadt   28 Feb 2011   
On a Khovanov homology of generalized Jones polynomials
ITO Noboru
The Seventh East Asian School of Knots and Related Topics, Higashi-Hiroshima,   12 Jan 2011   
A colored Khovanov bicomplex [Invited]
ITO Noboru
Special Thursday Seminar on Topology, Stony Brook University, Department of Mathematics and Institute for Mathematical Sciences   13 Dec 2010   
A colored Khovanov bicomplex [Invited]
ITO Noboru
Columbia Symplectic Geometry, Gauge Theory, and Categorification Seminar, Columbia University   6 Dec 2010   
On some versions of Khovanov homology [Invited]
ITO Noboru
Knots in Washington XXXI, The George Washington University   5 Dec 2010   
A colored Khovanov bicomplex [Invited]
ITO Noboru
16 Nov 2010   
Remarks on categorification of the colored Jones polynomial
ITO Noboru
24 Oct 2010   
Nanowords and Arnold invariants [Invited]
ITO Noboru
Seminario de Geometia Algebraica y Singularidades, Valladolid University   19 Oct 2010   
On a Khovanov bicomplex [Invited]
ITO Noboru
Conference on Singularities, Geometry and Topology, in honor of Sabir M. Gusein-Zade with occasion of his 60th birthday, including talks dedicated to the Memory of V. I. Arnold, EL Escorial   12 Oct 2010   
Spectral sequences for the colored Jones polynomial [Invited]
ITO Noboru
The 5th International Conference Japan-Mexico on Topology and its Applications, Colima University   28 Sep 2010   
A bicomplex and spectral sequences for a categorification of the colored Jones polynomial [Invited]
ITO Noboru
28 Aug 2010   
On Khovanov complexes [Invited]
ITO Noboru
KNOTS in Poland III, Stefan Banach International Mathematical Center   27 Jul 2010   
A bicomplex for Khovanov homology of the colored Jones polynomial” [Invited]
ITO Noboru
XIXth Oporto Meeting on Geometry,Topology and Physics, Categorificaiton, Algarve University   21 Jul 2010   
On Khovanov complexes [Invited]
ITO Noboru
CTQM and QGM Seminar, Aarhus University   21 Jun 2010   
On Khovanov complexes [Invited]
ITO Noboru
International Research Training Group 1529 Seminar, TU Darmstadt   1 Jun 2010   
Chain homotopy maps for Khovanov homology [Invited]
ITO Noboru
7 May 2010   
A bicomplex of Khovanov homology for colored Jones polynomial [Invited]
ITO Noboru
6 May 2010   
「Nanoword and nanophrases invariants of finite type」
ITO Noboru, Andrew Gibson
26 Mar 2010   
Chain homotopy maps of Khovanov homology [Invited]
ITO Noboru
International Workshop on Mathematical Fluid Dynamics, Waseda University   15 Mar 2010   

Education

 
 
 - 
2010
Waseda University