Speaker
Helen Wong
Description
In the case of a closed surface, there is a rich body of work describing how the Kauffman bracket skein algebra can be regarded as a quantization of Teichmuller space. In order to generalize to a surface with punctures, Roger and Yang defined a skein algebra with extra generators and relations that they conjectured to be a quantization of Penner's decorated Teichmuller space. In joint work with Han-Bom Moon, we resolve their conjecture by appealing to another algebra closely related to the decorated Teichmuller space, a cluster algebra for punctured surfaces first defined by Fomin, Shapiro, and Thurston.
