Convex bodies and algebraic properties of graded families of ideals

Time: 9:30 -- 11:00, June 25th, 2025

Venue: Room 612, A6

Abstract: We discuss how to understand various algebraic properties and invariants of graded families of ideals via associated convex bodies and regions. Particularly, we will extend the construction of Newton non-degenerate ideals and their Newton polyhedra to regular local rings, and investigate when simpler convex regions can replace the Newton-Okounkov bodies to give a more accessible approach to the Multiplicity = Volume formula.