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Monday, November 18, 2019
4:00 PM - 5:00 PM
Linde Hall 387

Algebra and Geometry Seminar

Skein theory, Hecke algebras, and elliptic curves
Peter Samuelson, Department of Mathematics, UC Riverside,

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.)

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