- 2019 - 2024 Research on 4-dimensional topology from the viewpoint of graphics and quandle theory
- 2018 - 2023 Solving the smooth unknotting conjecture in dimension four
- 2017 - 2022 Innovative research of geometric topology and singularities of differentiable mappings
- 2018 - 2021 Low-dimensional Topology: Knotted surfaces as real algebraic varieties
- 2016 - 2019 低次元トポロジー、ブレイド群の一般化と4次元の結び目理論
- 2014 - 2019 Research on 4-dimensional topology from the viewpoint of graphics and quandle theory
- 2017 - 2018 Innovation of singularity theory of mappings and new development of topology
- 2015 - 2018 カンドルおよびバイカンドルを用いた結び目と曲面結び目の研究
- 2012 - 2017 Solving the smooth unknotting conjecture in dimension four and its development
- 2012 - 2017 Topology of knots and 3-manifolds
- 2012 - 2017 Studies of knot theory and their applications
- 2011 - 2016 New developments of singularity theory of mappings
- 2011 - 2016 New developments in number theoretic geometry, topology, and algorithm
- 2013 - 2015 カンドルのブレイドホモロジー理論と結び目理論への応用
- 2012 - 2015 Quandles and discrete symmetric spaces
- 2010 - 2015 Geometric structure and combinatorial structure of 3-dimensional manifolds
- 2009 - 2014 Research on 4-dimensional topology from the viewpoint of graphics and quandle theory
- 2011 - 2013 Generalization of quandles and their applications
- 2009 - 2012 Solving the unknotting conjecture in dimension four and its development
- 2009 - 2011 Indiscrete representations of discrete groups
- 2009 - 2011 Studies of Knot Theory
- 2008 - 2011 4-MANIFOLDS AND RIEMANN SURFACES
- 2006 - 2009 Heegaard structures and geometric structures of 3-manifolds
- 2006 - 2008 多様体対への可微分写像に対する有限型不変量の定式化とその応用
- 2006 - 2008 不変量が自明な4次元多様体の研究
- 2005 - 2008 グラフィクスとカンドル理論の観点からの4次元トポロジーの研究
- 2005 - 2007 カンドルホモロジーと結び目不変量のバイカンドルへの一般化に関する研究
- 2004 - 2007 Smooth unknotting conjecture in dimension four and search for essence of mathematics
- 2004 - 2006 Geometry and topology of 4-manifolds
- 2003 - 2005 2次元結び目解け予想の解決
- 2002 - 2005 STUDY OF TOPOLOGICAL INVARIANTS FOR KNOTS AND THEIR APPLICATIONS
- 2003 - 2004 Developing monodromy descriptions and studying two-dimensional knots and braids by using quandles
- 2002 - 2004 Classification of 3-manifolds by link correspondence and knot theory
- 2001 - 2002 2次元結び目解け予想
- 2001 - 2002 2次元結び目とブレイド理論及びカンドル・コホモロジーの研究
- 2000 - 2002 Topological Study on the Degeneration Phenomena of Riemann Surfaces
- 1999 - 2001 STUDY ON KNOT INVARIANTS AND ITS APPLICATIONS
- 1998 - 1999 Monodromy calculus in low dimensional topology and "racks".
- 1997 - 1998 低次元の結び目とブレイドの構造の研究
- 1997 - 1998 STUDY ON KNOT INVARIANTS
- 1996 - 1997 結び目・絡み目とブレイドの高次元化に関する研究
- 1996 - 1996 変換群の幾何学
- 1995 - 1996 4次元多様体内の閉曲面とブレイド理論に関する研究
- 1994 - 1995 2次元ブレイドの研究
- 1994 - 1994 変換群の幾何学
- 1993 - 1994 2次元の結び目とブレイドの研究
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