Dagstuhl-Seminar — Triangulations in Geometry and Topology

The mathematical study of fundamental objects such as curves, embedded graphs, surfaces and 3-manifolds has a rich and old history. Research into their algorithmic and combinatorial properties, and underlying computational questions, on the other hand, is still young. From the complexity-theoretic side important open problems are hardness of realizability, fine-grained complexity of distance and similarity measure computations, existence of polynomial-time algorithms for flip distances, or approximability of such distances. Combinatorics and algebra come into play when dealing with associated polyhedral structures such as associahedra and secondary polytopes, and mapping class groups of surfaces. Moreover, applied fields such as trajectory analysis and machine learning yield new questions and perspectives.