* Title : Bangles, bracelets and bands

* Speaker : HyunKyu Kim (KIAS)

* Abstract : 

The Kauffman bracket skein algebra of an oriented surface S is an algebra generated by isotopy classes of framed links in the thickened surface S x (-1,1), with superposition product. It is a quantization of the SL2 character variety of the surface. I will recall several vector space bases of this algebra, given by bangles, bracelets or bands, and explain some remarkable phenomena and conjectures. In relation to these, I will try to touch on various topics like quantum cluster varieties and representation theory.