My CV is available here
Research Interests
My current interests within algebraic topology are to do with the study of principal G-bundles and their gauge groups (the group of G-equivariant bundle automorphisms of the total space of a principal bundle covering the identity map on the base space).
To be precise, I am interested in the case when the Lie group G has a discrete, path-connected centre. The central elements of G give rise to gauge transformations, and I am focused on studying when the gauge group admits a path between these transformations that arise from the central elements of G.
Pre-print
"Turning Vector Bundles", Melbourne 2022, with Diarmuid Crowley, Csaba Nagy and Huijun Yang.
Slides, Notes and Posters
Readers should beware of mistakes as many of these notes have not been carefully proofread (especially for those marked with an *asterisk*)
Notes:
Vector Fields on Spheres using Steenrod Squares, notes for a seminar given in the Cohomology Seminar, University of Melbourne
(Unfinished) The Theorem of Poincare and Hopf*, unfinished notes based on the book "Topology from the differentiable viewpoint" by Milnor
Cohomology Ring of CP^n*, notes for a seminar in the Graduate Topology Seminar, University of Melbourne
Slides and posters:
Turning Vector bundles, MSc Thesis presentation slides, University of Melbourne
Homology and Complexes*, a poster summary outlining the differences between simplicial, delta and CW complexes
Vector Fields on Manifolds, a poster giving an overview of the theorem of Poincare-Hopf relating the Euler characteristic to a geometric property of vector fields