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Geometry and Topology Seminar

Wednesday, April 20, 2016
3:00pm to 5:00pm
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The colored Jones polynomial and boundary slopes of pretzel knots
Christine Lee, NSF Postdoctoral Fellow, Mathematics, University of Texas at Austin,
The Slope Conjecture by Garoufalidis and the Strong Slope Conjecture, by Kalfagianni and Tran, relate the growth of the degrees of the colored Jones polynomial to the slopes and Euler characterstics of essential surfaces in the knot complement. In this talk, we present our recent result proving these conjectures for a class of 3-tangle pretzel knots. In particular, we will discuss how the use of the Hatcher-Oertel algorithm and the corresponding computation of the colored Jones polynomial in the proof suggest a framework for understanding these conjectures for more general knots. This is joint work with Roland van der Veen. 
 
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