Mauro Spera, Università Cattolica del Sacro Cuore, Brescia, Italy
Symplectic geometry, geometric quantization and the HOMFLYPT polynomial

(joint work with Antonio Michele Miti)

In this talk we survey the symplectic geometric approach to knot framing via Lagrangian submanifold theory and geometric quantization developed in Besana&S. (2006) and extend it, taking inspiration from Liu&Ricca (2012,2015), to achieve a geometric interpretation of the HOMFLYPT polynomial based on helicity only.

Besana A. and Spera M., On some symplectic aspects of knots framings,
J. Knot Theory Ram. 15 (2006), 883-912.

Liu X. and Ricca R.L., The Jones polynomial for fluid knots from helicity,
J. Phys A: Math. Theor. 45 (2012), 205501 (14pp).

Liu X. and Ricca R.L., On the derivation of the HOMFLYPT polynomial invariant for fluid knots,
J. Fluid Mechanics 773 (2015), 34-48.

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There will be a 20 minute discussion period / coffee break at the end of this talk.