This workshop will focus on recent interactions between contact/symplectic geometry, cluster algebras, and skein theory.
Legendrian knots/submanifolds and their Lagrangian fillings have recently been discovered to be intimately related to cluster algebras through either Floer theory or (equivalently) microlocal sheaf theory. This has opened up a large dictionary between Lagrangian fillings (and augmentation varieties) of Legendrian submanifolds and cluster algebras (including quantum Teichmüller theory). The time seems right for a large-scale interaction between the symplectic and cluster communities to further develop both fields using insights obtained from the other.
In a related direction, skein theory has also recently been tied to Floer theory and specifically symplectic field theory.
Skein theory plays a role in many parts of mathematics–invariants of low-dimensional manifolds and knots, quantum topology, representation theory–and is an important recurring theme for the long program. In the setting of Floer theory, skein theory is related to string topology, and the geometric insights from Floer theory may help shed more light on skein theory (for example, on some positivity questions). A goal of this workshop is to bring together experts in symplectic aspects of skein theory and string topology and experts in quantum topology in the same space.
This workshop will include a poster session; a request for posters will be sent to registered participants in advance of the workshop.
Roger Casals
(University of California, Davis (UC Davis))
Daniel Douglas
(Virginia Tech)
Ko Honda
(University of California, Los Angeles (UCLA))
Ian Le
(Australian National University)
Lenny Ng
(Duke University)
Angela Wu
(Bucknell University)
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