Department of Mathematics
Multivariable quantum invariants
of links arising from Lie superalgebras
Nathan Geer
Georgia Institute Of Technology
There are deep connections between quantum algebra and knot theory. Every representation of a semisimple Lie algebra gives rise to a quantum group invariant of knots. The Jones, Kauffman, and HOMFLY knot invariants are all examples of such invariants. Invariants arising from Lie algebras can be extended to Lie superalgebras. These new invariants are more powerful than invariants arising from Lie algebras and have interesting new properties. In this talk I will speak about multivariable invariants of links arising from finite dimensional modules of Lie superalgebra of classical type. In particular, I will start with a gentle introduction into knot theory. Then I will give the construction of the standard Reshetikhin-Turaev quantum group invariant of links and discuss how to modify this construction (in the case of Lie superalgebras) in order to define a non-trivial invariant of links. Finally, I will touch on how these invariants are related to other well known invariants including the multivariable Alexander polynomial and Kashaev's quantum dilogarithm invariants of links. I plan on making this talk accessible to a general mathematical audience.
All interested persons are welcome.