Newton-Okounkov Bodies and Minimal Models for Cluster Varieties

Explore a general procedure for constructing Newton-Okounkov bodies for line bundles on minimal models of cluster varieties in this 50-minute conference talk. Delve into applications for line bundles on Grassmannians and flag varieties, and discover how this approach recovers distinguished polytopes from representation theory, such as Gelfand-Tsetlin polytopes, Littelmann/Berenstein-Zelevisnky string polytopes, and Rietsch-Williams flow valuation Newton-Okounkov polytopes. Examine the construction details for Grassmannians, comparing the use of A and X cluster structures in creating Newton-Okounkov polytopes. Investigate the role of the Euler form of the dimer algebra, as employed by Jensen-King-Su and Baur-King-Marsh, in establishing an equivalence between the two types of polytopes and its significance in categorizing the cluster structure on the homogeneous coordinate ring of a Grassmannian.