Newton-Okounkov body, algebraic properties and invariant of graded families of monomial ideals

Time: 9:30 -- 11:00, June 14th, 2023.

Venue: Room 612, A6

Abstract: The Newton-Okounkov body of a graded family of monomial ideals is a natural generalization of the Newton polyhedron of a monomial ideal. We shall see how combinatorial data of the Newton-Okounkov body of a graded family of monomial ideals can be used to understand algebraic properties and invariant of the given family. We will focus on the Noetherian property of the Rees algebra, the analytic spread and the asymptotic regularity of families of monomial ideals.