Bio - David Sykes | Mathematics

Research Interests

I work on topics in CR Geometry with interest in techniques from Differential Geometry and their interplay with Several Complex Variables. I am curious about applications of Tanaka prolongation and related equivalence methods throughout differential geometry.

Academic Positions

Postdoctoral Research Fellow, Center for Complex Geometry, Institute for Basic Science, South Korea (2024–present)
Postdoctoral Researcher, Masaryk University, Czech Republic (2021–2024)

Education

Ph.D. in Mathematics, Texas A&M University (advisor: Igor Zelenko) (2021)
Bachelor of Science, Pure Mathematics, University of North Carolina at Greensboro (2015)
Bachelor of Music, Jazz Studies, University of North Carolina at Greensboro (2015)

Publications

Publications and more are listed on my Google Scholar and Orcid pages.

selcted publications

Models of 2-nondegenerate CR hypersurfaces in ℂᴺ

Jan Gregorovič, Martin Kolář, and David Sykes. Mathematische Annalen, 2025 DOI: https://doi.org/10.1007/s00208-025-03138-1
Homogeneous 2-nondegenerate CR manifolds of hypersurface type in low dimensions

David Sykes. Indiana University Mathematics Journal, 72(2), p.279–319
On geometry of 2-nondegenerate CR structures of hypersurface type and flag structures on leaf spaces of Levi foliations

David Sykes and Igor Zelenko. Advances in Mathematics, 2023 DOI: https://doi.org/10.1016/j.aim.2022.108850
New examples of 2-nondegenerate real hypersurfaces in ℂⁿ with arbitrary nilpotent symbols

Martin Kolář, Ilya Kossovskiy, and David Sykes. Journal of the London Mathematical Society, 2024 DOI: https://doi.org/10.1112/jlms.12962
Maximal Dimension of Groups of Symmetries of Homogeneous 2-nondegenerate CR Structures of Hypersurface Type with a 1-dimensional Levi Kernel

David Sykes and Igor Zelenko. Transformation Groups, 2024 DOI: https://doi.org/10.1007/s00031-022-09739-3
Models of CR Manifolds and Their Symmetry Algebras

Jan Gregorovič, Martin Kolář, Francine Meylan, and David Sykes. Advances in Applied Clifford Algebras, 2024 DOI: https://doi.org/10.1007/s00006-024-01341-y
A canonical form for pairs consisting of a Hermitian form and a self-adjoint antilinear operator

David Sykes and Igor Zelenko. Linear Algebra and its Applications, 2020 DOI: https://doi.org/10.1016/j.laa.2019.12.018

Preprints