SAITO, Mutsumi
 Research Field
 Algebra
 Position
 Professor
 Organization
 Department of Mathematics
 Research Interest
 Algebraic Analysis, Ring Theory
 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 Ahypergeometric 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.  Papers:
 [1] M. Saito, B. Sturmfels, N. Takayama,
Groebner deformations of hypergeometric differential equations,
Algorithms and Computation in Mathematics 6,
SpringerVerlag, Berlin, Heidelberg, New York, (2000).  [2] M. Saito, Isomorphism classes of Ahypergeometric systems,
Compos. Math., 128(3) (2001) 323–338.  [3] M. Saito, W. N. Traves, Finite generation of rings of
differential operators of semigroup
algberas, J. Algebra, 278 (2004) 76–103.  [4] M. Saito, Irreducible quotients of Ahypergeometric systems,
Compos. Math., 147(2) (2011) 613–632.  [5] M. Saito, Limits of Jordan Lie subalgebras,
J. Lie Theory, 27(1) (2017) 51–84.  Keywords
 Hypergeometric function, Ring of differential operators, Toric ideal