Wednesday, January 8 at 2:00pm to 3:00pm
Kaprielian Hall (KAP), 245
3620 South Vermont Avenue, Los Angeles, CA 90089
David Jordan, University of Edinburgh
Abstract: Skein modules are celebrated quantum invariants of three-manifolds: the skein module of M is the vector space spanned by tangles in M modulo local "skein" linear relations depending on a complex parameter q and resembling those which define the Jones polynomial. The classical limits of skein modules as q degenerates to +/- 1 recover interesting and well-studied moduli spaces of local systems called character varieties.
We learn a lot about skein modules simply by studying these classical degenerations and their associated symplectic geometry, using the tools of geometric representation theory. In this talk, I'll explain the general methods of stacks, Hamiltonian reduction, Poisson orders, and holonomicity, and I'll outline how these ideas enter into our recent proofs of the unicity and finiteness conjectures of Bonahon--Wong and Witten, respectively. The talk will be based on joint works with Iordan Ganev, Sam Gunningham and Pavel Safronov.