Australian Geometric Topology Webinar (AGTW)

AGTW Broadcast 

Date: Wednesday, 21 October 2026 

Time: 12noon-1pm 

Speaker: Lucy Tobin (University of Sydney) 

Location: SMRI Seminar Room (Macleay A12 Room 301) 

Title: Generating Random Manifolds with Grids and Gems 

Abstract: If you ask a topologist to name their favourite 3- or 4-manifold, chances are
they’ll give you a nice answer - something interesting, well-behaved and easy to
describe - but not really a generic one.  So we ask: is it possible to make a program -
a “press for random manifold” button - that can generate you something genuinely
generic, presented in a form you can work with computationally? This would both give
insight into what a “typical” manifold looks like, and be a useful tool in the
toolbox of the working low-dimensional topologist, for example when testing new
conjectures.  

I'll introduce a new approach to this random sampling problem for closed 3-manifolds, a
class of compact smooth 4-manifolds, and (potentially) all closed smooth 4-manifolds.
This involves sampling random links using grid diagrams, interpreting these links as
Kirby diagrams, and using a construction of Casali and Cristofori to build
triangulations of the corresponding 3- or 4-manifolds.  We can then discuss its
successes, complications, and early data and results.