- 2021 - 2024 Classification of ribbon 2-knots and their cross sectional ribbon 1-knots
- 2016 - 2019 The image by multilinear map to the real projective space and an application to the rank of tensors
- 2012 - 2016 Tensor rank problem and multivariate analysis of tensor normal distributions
- 2012 - 2015 Flexibilities of finite group actions on manifolds
- 2010 - 2014 Topological complexity and L-S theory
- 2008 - 2010 A study of analysis of high dimensional array data through computational algebraic statistical methods and it's application to statistical image analysis
- 2005 - 2007 A study of representations appeared as the tangential spaces of manifilds at fixed points
- 2003 - 2006 Application of A_∞-methods on topological invariants
- 2002 - 2004 A study of representations and finite group actions realizing a given fixed point set
- 1999 - 2000 Hopf invariants and their application
- 1996 - 1996 有限支配された空間と有限性障害の特徴づけ
- 1994 - 1994 同変有限性障害と代数的K-理論の研究
- 1992 - 1993 A study on pairings
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