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Friday, November 15, 2019
3:00 PM - 5:00 PM
Linde Hall 187

Geometry and Topology Seminar

GPV invariants and knot complements
Ciprian Manolescu, Department of Mathematics, Stanford University,

Gukov, Putrov and Vafa predicted (from physics) the existence of some 3-manifold invariants that take the form of power series with integer coefficients, converging in the unit disk. Their radial limits at the roots of unity should recover the Witten-Reshetikhin-Turaev invariants. Further, they should admit a categorification, in the spirit of Khovanov homology. Although a mathematical definition of the GPV invariants is lacking, they can be computed in many cases. In this talk I will discuss what is known about the GPV invariants, and their behavior with respect to Dehn surgery. The surgery formula involves associating to a knot a two-variable series, obtained by parametric resurgence from the asymptotic expansion of the colored Jones polynomial. This is based on joint work with Sergei Gukov.

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.