Watanabe Keiichi

2008 - 2011 Method of positive characteristic in Singularity Theory

2006 - 2009 Classification of isolated singularities by means of algebraic geometric studies of invariants

2006 - 2009 Research on the singularities of a variety

2005 - 2007 Singularity Theory via Frobenius morphism

2004 - 2006 Research for multiplicities and tight closures on singular points of positive characteristic

2001 - 2005 Singularity Theory via Commutative Ring Theory

2004 - 2005 Filtered blowing-up of local rings and algebraic geometric classification of singularities

2004 - 2005 Applications of tight closure and F-singularity to algebraic geometry

2002 - 2005 Research on singularities of a variety

2002 - 2003 On ring-theoretical properties of blow-up rings over singular points in positive characteristic

2002 - 2003 Filtered blowing-up of singularities and algebraic geometric properties of tangent cone

2001 - 2003 整閉イデアルの族の研究

2001 - 2003 Algebro-Geometric Method in Commutative Algebra

2000 - 2002 Study of relations and applications of Arithmetic Geometry to branches of Algebra

2000 - 2001 Research on ergodic theory and Perron-Frobenius operator

1998 - 2000 Characteristic p method in singularity theory

1995 - 1997 Applications of Frobenius map to Commutative Ring Theory and Algebraic Geometry

1994 - 1996 Commutative Artinian Algebras

1994 - 1996 Study on algebras and their representations

1995 - 1995 Upper bound graphとposetの関連について

1994 - 1994 F-rational Ringの研究

1992 - 1994 Algebra and Geometry on Algebraic Varieties

1993 - 1993 Frobenius写像の特異点への作用

1992 - 1992 数え上げ組合せ論の鎖数の研究

1991 - 1991 Intersection Graphの研究

1990 - 1990 有理特異点とFrobenius写像の作用

1989 - 1989 エントロピ-とブラクタルと無限行列の関連

1988 - 1988 状態監視保全の数理モデルとその最適性に関する研究

1987 - 1987 データベースを土台にした大学の数学における自習システムと言語の開発

1985 - 1986 On the Rang of Mordell-Well group of Elliptic curves.