I am a PhD student in the topology group at the University of Oxford, supervised by Marc Lackenby. Before this, I most recently worked at the Machine Learning Research Group, Data61, CSIRO in Australia, after completing my undergraduate degree at the Australian National University.
I am interested in low-dimensional and geometric topology, and in particular in triangulation complexity and the mapping class group.
My email is [firstname].[lastname]@maths.ox.ac.uk.
UMAP is a new dimension reduction technique that finds a representation with similar topological properties to the original data. I wrote up a set of notes on the mathematics behind UMAP, which is mostly category theory and topology, for people who have not seen much of these before.
You can download my notes on the mathematics of UMAP.
The mapping class group is an important algebraic invariant of a surface. Presentations of this group have wide applications to low-dimensional topology. I explicitly constructed Hatcher and Thurston’s finite presentation with Dehn twist generators for genus one and two surfaces. I also extended Bene’s chord slide generators from surfaces with connected boundary to those with disconnected boundary. This presentation arises from studying a cell decomposition of Teichmüller space whose vertices are fatgraph decorations of surfaces.The resulting fatgraph presentation of the mapping class group can be converted to one with chord slide generators. This chord slide presentation has potential applications to computing bordered Heegaard Floer invariants for open books with disconnected binding.
I am in the process of finishing off some of this work and writing it up in a (much) more concise form.