Workshop II: Contact Geometry, Cluster Algebras and Skein Theory
Workshop II: Contact Geometry, Cluster Algebras and Skein Theory supports experts through a research workshop to build connections among contact and symplectic geometry, cluster algebras, and skein theory.
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Funder: Institute for Pure and Applied Mathematics
Due Dates: October 26–29, 2026 (Workshop)
Funding Amounts:
Summary: A research workshop bringing together experts in contact and symplectic geometry, cluster algebras, and skein theory to develop connections across these fields.
Description
Run by the Institute for Pure and Applied Mathematics (IPAM) at UCLA, this workshop is part of the long program Quantum Topology, Character Varieties and Low-Dimensional Geometry. It explores connections between Legendrian knots and submanifolds, their Lagrangian fillings and augmentation varieties, and cluster algebras—including quantum Teichmüller theory—through Floer theory or microlocal sheaf theory.
The workshop also examines links between skein theory, Floer theory, symplectic field theory, and string topology. Its goal is to bring the symplectic and cluster communities together and connect experts in symplectic aspects of skein theory and string topology with experts in quantum topology. These exchanges aim to develop both fields and illuminate questions such as positivity in skein theory, with connections to knot and low-dimensional manifold invariants and representation theory.
