An algebraic introduction to the Kauffman bracket skein algebra (Helen Wong, CMC)

The Kauffman bracket skein algebra was originally defined as a generalization of the Jones polynomial for knots and links on a surface and is one of the few quantum invariants where the connection to hyperbolic geometry is fairly well-established.  Explicating this connection to hyperbolic geometry requires an understanding of the non-commutative structure of the skein algebra, especially at roots of unity.  We’ll present some of the known (and not known) properties of the skein algebra.  Highlights include the Chebyshev polynomials, quantum tori, $SL(2, \mathbb C)$ and other interesting algebraic objects.