Newton-Okounkov bodies arising from cluster structures and mutations on polytopes

Abstract: A toric degeneration is a flat degeneration from a projective variety to a toric variety, which can be used to apply the theory of toric varieties to other projective varieties. In this talk, we discuss relations among the following three constructions of toric degenerations: representation theory, Newton-Okounkov bodies, and cluster algebras. More precisely, we construct Newton-Okounkov bodies using cluster structures, and realize representation-theoretic and cluster-theoretic toric degenerations using this framework. We also discuss its relation with combinatorial mutations which was introduced in the context of mirror symmetry for Fano varieties. More precisely, we relate Newton-Okounkov bodies of flag varieties arising from cluster structures by combinatorial mutations. This talk is based on joint works with Hironori Oya and Akihiro Higashitani.

algebraic geometrycombinatoricsdifferential geometrygeometric topologyquantum algebrarepresentation theorysymplectic geometry

Audience: researchers in the topic

Legendrians, Cluster algebras, and Mirror symmetry

Series comments: Schedule
School: January 4–8, 2021
Conference: January 11–15, 2021