Research

Suspension splittings of 5-dimensional Poincaré duality complexes and their applications (2023) arXiv
with Tyrone Cutler and Tseleung So
Cohomology operations for moment-angle complexes and resolutions of Stanley-Reisner rings (2023) arXiv
with Ben Briggs, to appear in Transactions of the American Mathematical Society
Product decompositions of moment-angle manifolds and B-rigidity (2022) Canadian Mathematical Bulletin, arXiv
with Ben Briggs

Infinite families of higher torsion in the homotopy groups of Moore spaces (2022) Algebraic & Geometric Topology, arXiv
with Frederick R. Cohen and Yuxin Luo
Connected sums of sphere products and minimally non-Golod complexes (2020) arXiv
to appear in Fields Institute Communications volume on Toric Topology and Polyhedral Products
The fibre of the degree 3 map, Anick spaces and the double suspension (2020) Proceedings of the Edinburgh Mathematical Society, arXiv
A homotopy decomposition of the fibre of the squaring map on Ω3S17 (2018) Homology, Homotopy and Applications, arXiv

Unstable Homotopy Theory Surrounding the Fibre of the pth Power Map on Loop Spaces of Spheres (2018) PhD Thesis
Cohomology Operations and the Toral Rank Conjecture for Nilpotent Lie Algebras (2013) MSc Thesis

Slides from a talk (titled Equivariant formality of torus actions on moment-angle complexes) I gave this summer at the workshop Polyhedral Products: a Path Between Homotopy Theory and Geometric Group Theory at the ICMS in Edinburgh.
Recording and slides from a talk (titled Higher torsion in the homotopy groups of Moore spaces) I gave at the Advances in Homotopy Theory workshop at the University of Southampton's Centre for Geometry, Topology, and Applications (CGTA). This talk is based on joint work with Fred Cohen and Yuxin Luo.
Recording and slides from a talk I gave at the 2020 CMS Winter Meeting session on Homotopy Theory. My talk was called The homotopy type of the fibre of the pth power map on loop spaces of spheres and was about loop space decompositions and an unstable homotopy theoretic interpretation of the Kervaire invariant problem.
Recording of a talk I gave (titled The minimal Hirsch-Brown model for moment-angle complexes) at the Steklov International Seminar for Young Researchers "Algebraic, Combinatorial and Toric Topology". Here are slides from a similar talk at Western University's Geometry and Topology Seminar and Princeton's International Polyhedral Products Seminar. This is all based on joint work with Ben Briggs which aims to relate certain cohomology operations arising in toric topology with the minimal free resolutions of Stanley-Reisner rings.