On 8 December 2021 I gave a (virtual) talk in the Topology session of the 2021 meeting of the Australian Mathematical Society.
Title: A symplectic basis for 3-manifold triangulations
Abstract: Walter Neumann and Don Zagier in the 1980s introduced a symplectic vector space associated to an ideal triangulation of a cusped 3-manifold. We will discuss an interpretation for this symplectic structure in terms of the topology of the 3-manifold. This work, joint with Jessica Purcell, involves train tracks, Heegaard splittings, and is related to Ptolemy varieties, geometric quantisation, and the
A-polynomial.
Slides from the talk are below.
austms_talk_v2A Symplectic Basis for 3-manifold Triangulations, AustMS 2021