Skein algebra of a punctured surface (Helen Wong, CMC)

The Kauffman bracket skein algebra of a surface is at once related to quantum topology and to hyperbolic geometry. In this talk, we consider a generalization of the skein algebra due to Roger and Yang for surfaces with punctures. In joint work with Han-Bom Moon, we show that the generalized skein algebra is a quantization of Penner’s decorated Teichmuller space, which consists of complete metrics of the surface with extra decoration at the punctures. Interestingly, our proof relies on a connection between the skein algebra and the cluster algebras of tagged arcs due to Fomin, Shapiro, and Thurston.