Quantum Topology / Hopf Algebra Seminar

Louis H Kauffman
UIC
Coloring Alternating Knots Modulo a Prime Number
Abstract: This talk will give the proof of Mattman and Solis of the Kauffman/Harary conjecture: The Fox colorings of minimal alternating knot diagrams with prime determinant p have the property that distinct arcs in the diagram have distinct colors. A Fox coloring modulo p is an assigment of elements of Z/pZ to the arcs of the diagram such that if arc b overpasses the ends of arcs a and c (meeting at crossing) then a + c -2b = 0 mod p. This talk will be entirely self-contained with elementary linear algebra and some notions of graph theory as the only prerequisites.
Tuesday March 13, 2018 at 3:00 PM in SEO 612
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