SEMINÁRIO SIMPLÉTICO - Knot contact homology and the Alexander polynomial

Knot contact homology and the Alexander polynomial
Expositor:Luis Diogo
Instituição: Uppsala University
Data e Horário: 28/09/18 | 15:30h

RESUMO: Knot contact homology (KCH) is an invariant of knots in the 3-sphere, and its definition combines the dynamics of the geodesic flow on the sphere and pseudoholomorphic curves. Recent developments in mathematics and theoretical physics have unveiled surprising relations between KCH, mirror symmetry and large N duality (the latter relates colored HOMFLY polynomials and open Gromov-Witten invariants in the resolved conifold). This talk will have the more modest goal of explaining a formula relating KCH (more specifically, the augmentation polynomial) and the Alexander polynomial of the knot. We will begin with an introduction to KCH. This is joint work with Tobias Ekholm.