SAITO Mutsumi Specially Appointed Professor


Department of Mathematics
Research Interest
Algebraic Analysis, Ring Theory
Hypergeometric function, Ring of differential operators, Toric ideal

Research Activities

I work on rings of differential operators and their modules, especially the ring of differential operators on an affine toric variety and the system of A-hypergeometric equations whose systematic study was started by Gelfand, Kapranov, and Zelevinsky.

As an algebraic torus acts on these objects, they have some combinatorial descriptions, and they are related to various subjects such as integer programming, hyperplane arrangements, and representation theory. I mostly study them from the combinatorial features.


  • M. Saito, B. Sturmfels, N. Takayama,
    Groebner deformations of hypergeometric differential equations,
    Algorithms and Computation in Mathematics 6,
    Springer-Verlag, Berlin, Heidelberg, New York, (2000).
  • M. Saito, Isomorphism classes of A-hypergeometric systems,
    Compos. Math., 128(3) (2001) 323–338.
  • M. Saito, W. N. Traves, Finite generation of rings of
    differential operators of semigroup
    algberas, J. Algebra, 278 (2004) 76–103.
  • M. Saito, Irreducible quotients of A-hypergeometric systems,
    Compos. Math., 147(2) (2011) 613–632.
  • M. Saito, Limits of Jordan Lie subalgebras,
    J. Lie Theory, 27(1) (2017) 51–84.