I will define conical symplectic singularities and give some examples. Then I’ll discuss their quantizations.

Abstract:  We define a family of Turaev-Viro type invariants of hyperbolic 3-manifolds with totally geodesic boundary from the 6j-symbols of the modular double of U_q(sl(2; R)), and prove that these invariants decay exponentially with the rate the hyperbolic volume of the manifolds and with the “1-loop term” the adjoint twisted Reidemeister torsion of the double of the manifolds. This is a joint work with Tianyue Liu, Shuang Ming, Xin Sun and Baojun Wu.