Research keywords (9)：
Lipschitz equivalence
, blow-analytic invariant
, blow-Nash triviality
, directional properties of singular spaces
, Sequense selection property
, equisingularity problem of real algebraic singularities
, motivic type invariants of real analytic singularities
, Real Algebraic Geometry
, Singularity Theory
Research theme for competitive and other funds (28)：
2020 - 2024 Structural stability problem of real algebraic maps and its application
2014 - 2019 Research on global properties of algebraic singularities
2011 - 2013 Geometry of analytic singularities
2008 - 2010 特異点の不変量の研究
2006 - 2007 Equisingularity Problems for Real Algebraic Singularities and Real Analytic Singularities
2005 - 2006 Research of real algebraic geometry by model theory
2004 - 2006 Structures of sets related to differentiability
2003 - 2006 Geometry of singularities of mapping II
2003 - 2005 特異空間の同程度特異性問題
2001 - 2002 Research on triviality of real singularities
2000 - 2002 STUDY OF SEMIGROUPS OF SETS OF VALUATIONS DEFINED BY EXCEPTIONAL COMPONENTS
1999 - 2002 Geometry of singularities of maps
1998 - 2000 Research on real algebraic singularities
1995 - 1995 有限群の準素な自己同型と指標の研究
1994 - 1994 実代数的集合族のmodified Nash thiialityについて
1993 - 1993 偏微分方程式論における一意性の研究
1993 - 1993 微分解析における同値関係の研究
1992 - 1992 有限群の自己同型の研究
1992 - 1992 楕円曲線上の有理点の研究
1991 - 1991 実解析関数の特異点の研究
1991 - 1991 準正規環と弱正規環の研究
1990 - 1990 解析関数の有限分割問題
1989 - 1990 Uniqueness of Solutions of Partial Differential Equations
1989 - 1989 群の構造の研究
1988 - 1988 不定方程式の解の研究
1987 - 1988 Research for Commutative Ring Theory
1985 - 1986 Investigation of unstable homotopy theory
特異点の種々の同値関係の相互関係の総合的研究
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Papers (41)：
Karim Bekka, Satoshi Koike. Characterisations of V-sufficiency and C^0-sufficiency of relative jets. Hokkaido Mathematical Journal. 2024. 53. 1. 1-50
Karim Bekka, Satoshi Koike. On the relative Kuo condition and the second relative Kuo condition. Topology and its Applications. 2022. 313. 107980-107980
Satoshi Koike, Laurentiu Paunescu. Stabilisation of geometric directional bundle for a subanalytic set. Topology and its Applications. 2022. 313. 107988-107988
Satoshi Koike, Laurentiu Paunescu. On finiteness theorems of polynomial functions. European Journal of Mathematics. 2022
Karim Bekka, Satoshi Koike. Equivalence of Kuo and Thom quantities for analytic functions. Proceedings of the Japan Academy. 2021. 97. 3. 19-24
Koike Satoshi. Finiteness on semialgebraic types of Nash mappings defined over a Nash surface. RIMS Kokyuroku. 2015. 1948. 1-5
小池 敏司. 実解析的特異点の不変量 (フォーラム 現代数学のひろがり 特異点の世界--その広さと豊かさ). 数学のたのしみ : have fun with mathematics. 2005. 2005. 80-93
Koike Satoshi. THE BRIANCON-SPEDER AND OKA FAMILIES ARE NOT BILIPSCHITS TRIVIAL (Several topics in singularity theory). RIMS Kokyuroku. 2003. 1328. 165-173
Koike Stoshi. A problem on blow-analytic sufficiency of jets (Singularity theory and Differential equations). RIMS Kokyuroku. 1999. 1111. 165-167
Bekka Karim, Koike Satoshi. The Kuo condition, Thom's type inequality and (c)-regularity. RIMS Kokyuroku. 1996. 952. 41-49
Seventh Japanese-Australian Workshop on Real and Complex Singularities
Romanian Journal of Pure and Applied Mathematics, Tome LXIV No. 4 2019
Proceedings of the sixth Japanese-Australian workshop on Real and Complex Singularities
Saitama Mathematical Journal, Vol. 31 2017
The Fifth Japanese-Australian Workshop on Real and Complex Singularities
Romanian Journal of Pure and Applied Mathematics, Tome LX No. 4 2015
Topics on real and complex singularities (JARCS4)
World Scientific Publishing Co. Pte. Ltd. 2014
The Japanese-Australian Workshop on Real and Complex Singularities - JARCS III
Proceedings of the Centre for Mathematics and its Applications, Australian National University, 43 2010
