GENERATING RANDOM MANIFOLDS WITH GRIDS AND GEMS
GENERATING RANDOM MANIFOLDS WITH GRIDS AND GEMS
Data evento : 09 March 2026 - 14.30
Dove: aula M1.4
Speaker: Dott. Lucy Tobin (University of Sydney)
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 resource for testing conjectures.
I’ll introduce a new approach to this random sampling problem for closed 3-manifolds, a class of compact 4-manifolds, and (potentially) all closed 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 gems of the corresponding 3- or 4-manifolds. We can then discuss its successes, complications, and early data and results.