For zoom details contact Bathel, Ozornova, Ray, Teichner.
I will give a survey on 3-manifolds and their triangulations (following Thurston),
and their combinatorics encoded in their NZ matrices. These were originally used
to compute hyperbolic volumes and Chern-Simons invariants, and more recently
have been used to define quantum invariants of 3-manifolds such as the 3D-index.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/TopologySeminar