My interests are in differential geometry. I am currently researching manifolds whose curvature tensors have large nullity distributions and so are flat in most directions.
J. Van Hook (2024), On the Geometry of Conullity Two Manifolds, Differential Geometry and its Applications, 92, 102081, DOI: 10.1016/j.difgeo.2023.102081.
E. Cartee, A. Farah, A. Nellis, J. van Hook, A. Vladimirsky (2023), Quantifying and managing uncertainty in piecewise-deterministic Markov processes, SIAM/ASA Journal on Uncertainty Quantification, 11:3, 814-847, DOI: 10.1137/20M1357275.
D. Clark, S. Mancini & J. Van Hook (2020) Misére Tic-Tac-Toe on Projective Binary Steiner Triple Systems, The American Mathematical Monthly, 127:5, 411-426, DOI: 10.1080/00029890.2020.1715706.