Tim Magee：Convexity in tropical spaces + compactifications of cluster varieties
2020-12-03 Online Algebraic Geometry Seminar
Tim Magee - 伯明翰大学
Convexity in tropical spaces and compactifications of cluster varieties
Cluster varieties are a relatively new, broadly interesting class of geometric objects that generalise 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 generalises 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. Time permitting, I'll conclude with two exciting applications of this more general notion of convexity: 1) an intrinsic version of Newton-Okounkov bodies and 2) a possible cluster version of a classic toric mirror symmetry construction due to Batyrev. Based on joint work with Man-Wai Cheung and Alfredo Nájera Chávez.
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