Mathematics Colloquia and Seminars

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Chern-Simons knot invariants can be described in terms of Hilbert spaces of states associated with two-dimensional surfaces and linear operators associated with knots. In the case of genus 1 surface, this description admits a one-parameter deformation that is called refined Chern-Simons theory. It is natural to wonder if such deformations exist for higher genus surfaces. In this talk we will describe without proof an explicit construction of refined knot operators in genus 2. These operators pass many non-trivial checks such as modularity and topological invariance.