Newton-Okounkov Bodies for Minuscule Homogeneous Spaces and Beyond

Explore the mathematical theory of Newton-Okounkov bodies in this advanced seminar talk by Charles Wang from the University of Michigan, presented at the Institute for Advanced Study's Special Year Seminar II. Delve into the construction of Chevalley polytopes from triples consisting of homogeneous spaces, dominant weights, and reduced expressions. Learn how these constructions yield combinatorial interpretations through minuscule posets when working with minuscule weights, resulting in Newton-Okounkov bodies with the integer decomposition property. Discover ongoing research and conjectures extending beyond the minuscule case, illustrated through numerous examples in this nearly two-hour mathematical exploration scheduled for April 3, 2025.