On 14 September 2022 I gave a talk (in person!) in the Monash Topology seminar.
Title: A symplectic approach to 3-manifold triangulations and hyperbolic structures
Abstract: In the 1980s, Neumann and Zagier introduced a symplectic vector space associated to an ideal triangulation of a cusped 3-manifold, such as a knot complement. We give an interpretation for this symplectic structure in terms of the topology of the 3-manifold, via intersections of certain curves on a Heegaard surface. We also give an algorithm to construct curves forming a symplectic basis for this vector space. This approach gives a description of hyperbolic structures on a knot complement via Ptolemy equations, which can be used to calculate the A-polynomial. This is joint work with Jessica Purcell and Joshua Howie.
Slides from the talk are below22-09-14_monash_talk