Newton-Okounkov bodies are convex bodies (which are often polyhedral) which encode information about algebraic varieties. Recent work suggests that the theory of Newton-Okounkov bodies is intimately connected with certain constructions in algebraic geometry arising from cluster algebras. The aim of this project is to explore the relation between these two areas .
Impact
The connections between Newton-Okounkov bodies and cluster algebras has significant potential consequences for multiple research areas, including: representation theory, symplectic geometry (particular, in the construction of integrable systems), and algebraic geometry.
Student Experience
Some graduate students and postdocs are involved in this project.
