Algebraic Geometry Seminar: "Convexity in tropical spaces and intrinsic NO bodies for cluster varieties"
Abstract: Cluster varieties are a relatively new, broadly interesting class of geometric objects that generalize toric varieties. Convexity is a key notion in toric geometry. For instance, projective toric varieties are defined by convex lattice polytopes. In this talk, I'll explain how convexity generalizes to the cluster world, where "polytopes" live in a tropical space rather than a vector space and "convex polytopes" define projective compactifications of cluster varieties. I'll then describe how this convexity notion leads to an intrinsic notion of Newton-Okounkov body for divisors on compactified cluster varieties. Based on joint work with Man-Wai Cheung and Alfredo Nájera Chávez, and ongoing joint work with Lara Bossinger, M-W Cheung, and A Nájera Chávez.
Host: Ben Wormleighton