QM Research Seminar: Skein relations in algebra and geometry

Speaker: Peter Samuelson (UC Riverside)


Abstract:
The Homflypt skein relations were originally used in the 90's to define polynomial invariants of knots in S^3. In this talk we describe several other ways they arise in algebra and geometry: intertwiners for certain quantum group representations, commutator relations in quantum groups, deformation quantization of trace functions on character varieties, commutator relations in Hall algebras of Fukaya categories of surfaces, and higher dimensional Heegaard-Floer homology of configuration spaces of points in cotangent bundles to surfaces. This will be a survey style talk; in particular, no significant prior knowledge of these topics will be assumed, and the precision of the statements will decrease monotonically as the talk progresses. Our main goal is to describe a nonobvious common theme in these topics.