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On the Generalized Catalan Numbers and the Eynard Orantin Topological Recursion


Speaker: Axel Saenz, UC Davis
Location: 2112 MSB
Start time: Tue, Apr 15 2014, 2:10PM

The Eynard-Orantin Topological Recursion is a formula that produces a family of symmetric differentials, indexed by two natural indices (g,n), on a curve \mathcal{C}. Current research is focusing on the case when the \mathcal{C} is the zero locus of the A-polynomial of a knot K. It is conjectured that the family of symmetric differentials given by the EOTR formula will produce an assymptotic expansion of the colored Jones polynomial of the knot K. As such, this is not well understood now. Thus, the presenter wishes to gain further understanding by presenting a well-understood example of the theory.