Email higashitani(
Algebraic combinatorics, Commutative ring theory
Keywords lattice polytopes, Ehrhart theory, graded commutative algebra

I study lattice polytopes. I'm particularly interested in the Ehrhart polynomial of a lattice polytope, which is the enumerative function on the number of lattice points contained in a lattice polytope. Moreover, I'm also working on lattice polytopes appearing in the context of commutative ring theory and algebraic geometry. For example, for a toric ring, which is a kind of graded commutative algebra arising from a lattice polytope, or a toric Fano variety corresponding to a Fano polytope (a kind of lattice polytopes), I try to obtain some properties of the original algebraic objects via combinatorial discussions on the corresponding lattice polytopes.