Algebra and Combinatorics Seminar

Speaker: Linhui Shen (Michigan State University)

Title: Skein algebras on punctured surfaces

Abstract: Skein algebras are generated by webs on thickened surfaces, subject to local skein relations that resolve crossings into simpler diagrams. In this talk, we construct a natural generalization of the Roger-Yang skein algebras, incorporating new skein relations associated with punctures on surfaces. As an application, we obtain a new quantization of the decorated higher Teichmuller spaces $\mathcal{A}{G,S}$ introduced by Fock and Goncharov. If time permits, we will also discuss connections with the duality conjecture for cluster algebras. This is joint work in progress with Zhe Sun and Daping Weng.