Research

Papers and Preprints

• The Morse index of quartic minimal hypersurfaces, with Jesse Madnick & Uwe Semmelmann. arXiv:2310.19404.

• Static solutions to symplectic curvature flow in dimension 4. arXiv:2310.00143.

• A Spinorial Hopf Differential for Associative Submanifolds, with Jesse Madnick. arXiv:2305.14508 Submitted.

• Associative Submanifolds of Squashed 3-Sasakian Manifolds, with Jesse Madnick. arXiv:2208.10622. Submitted.

• Quadratic closed G2-structures.  Journal of the London Mathematical Society 107 (2023) 1110-1171 (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).

PhD Thesis

My 2019 Duke University PhD thesis, entitled Seven-Dimensional Geometries With Special Torsion, may be found here. The material in Part 1 has been incorporated into the papers Closed G2-structures with conformally flat metric and Quadratic closed G2-structures.

Videoed Talks

• Closed G2 -structures with conformally flat metric, Simons Collaboration on Special Holonomy: Progress and Open Problems 2020, Sept. 2020

• Quadratic closed G2 -structures, Virtual seminar on geometry with symmetries, July 2020

• Quadratic closed G2 -structures, Simons Collaboration on Special Holonomy: Progress and Open Problems 2019, Simons Center, Sept. 2019

• Quadratic closed G2 -structures, G2 Geometry & Related Topics, Casa Matemática Oaxaca, May 2019

• SO(4)-structures on 7-manifolds, Simons Collaboration on Special Holonomy: Progress and Open Problems 2017, Simons Center, Sept. 2017