String-Math Seminar: Integrability of higher genus refined Chern-Simons theory

Seminar | May 8 | 2-3 p.m. | 402 LeConte Hall

 Shamil Shakirov, Harvard University

 Department of Mathematics

It is known that Chern-Simons topological quantum field theory admits a one-parameter deformation – refinement – in the genus 1 sector. I will tell about a genus 2 generalization of this fact. Just like in the torus case, the crucial role is played by an interesting quantum-mechanical integrable system, which is a genus 2 generalization of Ruijsenaars-Schneider-Macdonald system. The knowledge of this quantum mechanics allows us to prove mathematically the corresponding mapping class group action, which is a genus 2 generalization of SL(2,Z)