Skeins, clusters, and character sheaves
De David Jordan
Apparaît également dans la collection : Symplectic representation theory / Théorie symplectique des représentations
Skein algebras are certain diagrammatically defined algebras spanned by tangles drawn on the cylinder of a surface, with multiplication given by stacking diagrams. Quantum cluster algebras are certain systems of mutually birational quantum tori whose defining relations are encoded in a quiver drawn on the surface. The category of quantum character sheaves is a $q$-deformation of the category of ad-equivariant $D$-modules on the group $G$, expressed through an algebra $D_q (G)$ of “q-difference” operators on $G$. In this I talk I will explain that these are in fact three sides of the same coin – namely they each arise as different flavors of factorization homology, and hence fit in the framework of four-dimensional topological field theory.
![$k$-sum free sets in $[0,1]$](/media/cache/video_light/uploads/video/2015-09-10_de_Roton-video--19cf70874d3c5af7378c268cab865b06.jpg)
