Algebra and Geometry Seminar

Skein theory can be viewed as a machine for producing algebras from surfaces and modules from 3-manifolds. We present the "type A" skein algebra of the torus, and show it is the t=q specialization of an algebra known as (1) the Hall algebra of coherent sheaves over an elliptic curve, (2) the limit of gl_n spherical double affine Hecke algebras. We then present the "type BCD" skein algebra of the torus -- in this case it is not clear what the analogue of (1) or (2) are. (Joint work with Morton and Pokorny.)