Francis Bonahon: Character varieties of surfaces and Kauffman brackets.
Abstract: My talk will involve two concepts which are apparently
very different. The character variety of a surface S, consisting
of homomorphisms from the fundamental group of S to a Lie group G,
arises in many different branches of mathematics. The classical
Kauffman bracket is an invariant of knots and links in space,
closely related to the Jones polynomial. When G = SL_2(C), Turaev
showed that the character variety can be quantised by a
generalisation of Kauffman brackets to the surface S. I will
discuss the classification problem for Kauffman brackets on S,
with results, conjectures and interesting examples.