Peter Samuelson, UC Riverside

Abstract: There is a sequence of inclusions "Hecke algebra --> affine Hecke algebra --> double affine Hecke algebra.'' In this talk we propose that skein theory gives a correspondence between this sequence and the sequence of inclusions "disk --> annulus --> punctured torus.'' We start by giving definitions of both sides of this correspondence, and will survey some previously known relationships between various Hecke algebras and skein theory as well.