On the Huynh-Le Quantum Determinant and the Head and Tail of the Colored Jones Polynomial

Geometry Topology Seminar
Friday, April 22, 2011 - 2:05pm for 1 hour (actually 50 minutes)
Skiles 269
C. Armond – Louisiana State University
Thang Le
In this talk I will describe how the quantum determinant modelof the Colored Jones polynomial, developed by Vu Huynh and Thang Le can beinterpreted in a combinatorial way as walks along a braid. Thisinterpretation can then be used to prove that the leading coefficients ofthe colored Jones polynomial stabalize, defining two power series calledthe head and the tail. I will also show examples where the head and tailcan be calculated explicitly and have applications in number theory.