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Wednesday, February 24, 2016
3:00 PM - 4:00 PM

Noncommutative Geometry Seminar

Kauffman Brackets on Surfaces
Francis Bonahon, Professor, Mathematics, USC,

Kauffman brackets on a surface are quantum deformations of homomorphisms from the fundamental group of the surface to the Lie group SL_2(C). A fundamental example arises from Witten's topological quantum field theory interpretation of the Jones polynomial of knots in 3-dimensional manifolds. I will discuss properties of finite-dimensional Kauffman brackets when the quantum parameter q is a root of unity. This will include the construction of invariants, existence properties, and uniqueness theorems and conjectures.

For more information, please contact Farzad Fathizadeh by email at farzadf@caltech.edu or visit http://www.math.caltech.edu/~ncg/.