Place: N820
Title: Turaev-Viro invariant from the modular double of UqSL(2;R)
Abstract: In this talk we introduce recent collaboration work with Shuang Ming, Xin Sun, Baojun Wu, and Tian Yang. 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 Uqsl(2;R), and prove that these invariants decay exponentially with the rate the hyperbolic volume of the manifolds.
Place: N933
Title: Homotopy theoretic properties of gyrations
Abstract: If M is a manifold, a gyration is a surgery on M\times S^k for some positive integer k. These appear prominently in work of Gitler-Lopez de Medrano on intersections of quadrics and recent work of Duan on the classification of certain types of manifolds. We will discuss homotopy theoretic properties of gyrations, such as loop space decompositions and classifications of homotopy types depending on how the surgery may be twisted by a nontrivial diffeomorphism. This is based on joint projects with Ruizhi Huang and Sebastian Chenery.