I am a Van Vleck Visiting Assistant Professor at UW Madison.
My research interests are in differential geometry and the geometry of partial differential equations. I am especially interested in the geometry of manifolds with special holonomy.
I got my PhD in mathematics at Duke University in May 2019 working under the supervision of Robert Bryant. I was a graduate student participant in the Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics. After getting my PhD I was a CIRGET postdoctoral fellow based at Université du Québec à Montréal from 2019-2021, and I taught at McGill University.
Papers and Preprints
Associative Submanifolds of Squashed 3-Sasakian Manifolds, with Jesse Madnick. arXiv:2208.10622. Submitted.
Quadratic closed G2-structures. To appear in Journal of the London Mathematical Society (preprint available at arXiv:2006.14155).
The DT-instanton equation on almost Hermitian 6-manifolds, with Gonçalo Oliveira. Communications in Mathematical Physics 388 (2021) 819–844 (preprint available at arXiv:2006.13399).
Associative Submanifolds of the Berger Space, with Jesse Madnick. To appear in Communications in Analysis and Geometry (preprint available at arXiv:2003.13169).
Closed G2-structures with conformally flat metric. arXiv:2002.01634 (Feb 2020) Submitted.
The Mean Curvature of First-Order Submanifolds in Exceptional Geometries with Torsion, with Jesse Madnick. Annals of Global Analysis and Geometry 59 (2021) 27–67 (preprint available at arXiv:1909.08119).
The Mean Curvature of Special Lagrangian 3-folds in SU(3)-Structures, with Jesse Madnick. Journal of Geometry and Physics 162 (2021) (preprint available at arxiv:1905.03713).
Gauge Theory on Aloff-Wallach Spaces, with Gonçalo Oliveira. Geometry & Topology 23 (2019) 685–743 (preprint available at arXiv:1610.04557).
Articles in preparation
G2 geometry of hypersurfaces in quaternion-Kahler 8-manifolds
Static solutions to symplectic curvature flow in dimension 4