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Algebras of Wilson loops on genus g surfaces

Mathematical Physics & Probability

Speaker: Shamil Shakirov, Harvard University
Location: 2112 MSB
Start time: Wed, Mar 7 2018, 3:10PM

For every closed oriented genus g surface Chern-Simons TQFT gives rise to an interesting algebra - the algebra of operators inserting Wilson loops. We describe them explicitly for genus 1 and 2 and show that the respective mapping class groups act by their automorphisms. Interestingly, both algebras admit a 1-parameter deformation - corresponding to refined Chern-Simons theory -- that respects this action