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Refined Chern-Simons theory in genus two

QMAP Seminar

Speaker: Shamil Shakirov, Harvard
Location: 2112 MSB
Start time: Thu, Dec 10 2015, 3:10PM

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.