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1.05pm - 2.30pm
in
Carslaw 709 on Thursday 9 August 2001
with a short break around 1.50pm
Ruibin Zhang
Quantum Groups and Knots
Quantum groups were originally introduced to describe symmetries of
two-dimensional integrable models in physics, but they also turned
out to have major applications in many areas of mathematics. This
talk discusses some aspects of quantum groups and their applications
to knots and three-manifolds. We first explain what a quantum group is,
and examine its structure and representations. We then demonstrate
how to construct topological invariants of knots from quantum groups,
and to extend such knot invariants (at roots of unity) to topological
invariants of three-manifolds. Finally we discuss a conjectural
relationship
between the quantum group invariants of knots and the Gromov-Witten
theory recently suggested in the physics literature.
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