Convex bodies and graded families of monomial ideals

Abstract: We show that the mixed volumes of arbitrary convex bodies are equal to mixed multiplicities of graded families of monomial ideals and to normalized limits of mixed multiplicities of monomial ideals. This result evinces the close relationship between the theories of mixed volumes from convex geometry and mixed multiplicities from commutative algebra. This is joint work with Jonathan Montaño.

Time permitting, we will also speak about some joint work with Fatemeh Mohammadi and Leonid Monin regarding "multi-graded algebras and multi-graded linear series".

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

Series comments: Note: To get meeting ID,fill the Google form on the web-site of the series sites.google.com/view/virtual-comm-algebra-seminar/home