By a result of Agol and Guéritaud, a transitive pseudo-Anosov flow F on a closed three-manifold N, along with a certain collection O of its closed orbits, determines a veering triangulation V of N - O that encodes F. Together with Henry Segerman, we devised and implemented an algorithm that takes as an input V and a closed orbit c of F that is not in O, and returns a veering triangulation of N - O - c that also encodes F. I will discuss the main ideas behind the algorithm, its key challenges, and its role in collecting experimental evidence for certain conjectures about pseudo-Anosov flows.

For a Lie group G, the G-skein module of a 3-dimensional manifold M is a fundamental object in Witten’s interpretation of quantum knot invariants in the framework of a topological quantum field theory. It depends on a parameter q and, when this parameter q is a root of unity, the G-skein module contains elements with a surprising “transparency” property, in the sense that they can be traversed by any other skein without changing the resulting total skein. I will describe some (and conjecturally all) of these transparent elements in the case of the special linear group SL_n. The construction is based on the very classical theory of symmetric polynomials in n variables.  

A relaxed-pace seminar on impromptu subjects related to the interests of the audience. Everyone is welcome. The subjects are geometry, probability, combinatorics, dynamics, and more!