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Introduction

Satoshi Murai
Associate Professor

Satoshi Murai

  • Pure and Applied Mathematics
  • Combinatorial Mathematics

Theme

Combinatorics and Commutative Algebra

My research area is combinatorics and commutative algebra. In particular, I am interested in combinatorial properties of simplicial complexes and algebraic properties of Stanley-Reisner rings.

Commutative algebra is a branch of algebra which mainly studies ideals and rings defined by polynomials. On the other hand, simplicial complexes appear in elementary topology. Although the origin of simplicial complexes comes from topology, they are currently of interest in combinatorics, and the study of face numbers of simplicial complexes is a common research topic in enumerative combinatorics. Around 1975, Richard Stanley found a beautiful relation between combinatorial properties of simplicial complexes and algebraic properties of certain rings which are currently called Stanley-Reisner rings. After the Stanley's work, the theory of Stanley-Reisner rings has been developed very much and now it appears in many topics relating to algebra and combinatorics.

Currently, I am interested in face numbers of polytopes, triangulated manifolds, simplicial cell complexes. My main research tool is commutative algebra, but I am also interested in topological and geometric combinatorics of these objects.

Career summary

2008 Ph.D., Osaka University
2008 Osaka University, Research Fellow of the Japan Society for the
Promotion of Science
2009 Kyoto University, Research Fellow of the Japan Society for the
Promotion of Science
2009 Yamaguchi University, Lecturer
2013 Yamaguchi University, Associate Professor
2014 Osaka University, Associate Professor

Contact

  • E-mail : s-murai@ist.
  • Tel : S5899

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