Applications of the Relation Between Cluster Algebras and Symplectic Topology - Part 2

Explore applications of the relationship between cluster algebras and symplectic topology in this third talk of the Western Hemisphere Virtual Symplectic Seminar series. Delve into consequences of moduli of Lagrangian fillings having coordinate rings that are cluster algebras. Discover how this connection leads to detecting infinitely many Lagrangian fillings and closed Lagrangian surfaces in simple Weinstein 4-folds, as well as the existence of holomorphic symplectic structures on these moduli. Learn about applications to cluster algebras using symplectic topology, including constructing cluster algebra structures on coordinate rings of Richardson varieties, the existence of Donaldson-Thomas transformations, and geometric examples explaining quasi-cluster structures. Engage with questions on topics such as finite Lagrangian fillings for links, additional structures for holomorphic symplectic manifolds, identifying exact Lagrangian fillings from weaves, and braids for dual cluster varieties.

Yoon Jae Nho: why do you expect only finitely many fillings for these links?
Jae Hee Lee: I have a naive question from part 2: can our holomorphic symplectic manifold be equipped with even more structure such as a hyperKahler metric, or a holomorphic Lagrangian fibration...?
Yoon Jae Nho: when do we know a given exact Lag filling comes from a weave?
Jae Hee Lee: From part 3, may I ask what the braid looks like for the dual cluster variety?