- 2009 - 2012 優秀環とその周辺の研究
- 2009 - 2012 Research on integral closure and related topics
- 2005 - 2008 Clarifying the basic theory of USD-sequences and their applications to the Kawasaki's theory of Macaulayfications
- 2003 - 2005 Numerical equivalence on Chow groups of local rings and its applications
- 2002 - 2004 Refinement of Iwasawa theory and its applications
- 2001 - 2003 Study of blowing-aps.
- 2000 - 2003 The basic theory of USD-sequences and the ring theoretical structure of Rees algebras
- 2000 - 2002 Research on Dutta multiplicity and Roberts ring
- 2000 - 2001 Arithmetic Study of Interactions of Galois groups and anabelian geometry
- 1999 - 2001 Research on arrangements of hyperplanes
- 1998 - 1999 Basic researchs on USD-sequences and its applications to improvements of singularities
- 1998 - 1999 Exterior Galois representations in fundamental groups and associated arithmetic phenomena
- 1998 - 1999 Data Computation and Software Development in Number Theory by Computers
- Excellent rings`
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