on the arXiv – published in the Proceedings of the Conference on Gromov-Witten Theory, Gauge Theory and Dualities, ANU/Kioloa, January 2016.
Abstract: This article is an exposition of a body of existing results, together with an announcement of recent results. We discuss a theory of polytopes associated to bipartite graphs and trinities, developed by Kálmán, Postnikov and others. This theory exhibits a variety of interesting duality and triality relations, and extends into knot theory, 3-manifold topology and Floer homology. In recent joint work with Kálmán, we extend this story into contact topology and contact invariants in sutured Floer homology.
Local pdf available here (703 kb).polytopes_dualities_floer_homology