Peter Crooks

Mathematics and Statistics

Assistant Professor

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Contact Information

Office Location: Animal Science (ANSC) 312
Phone: (435) 797-1536

Educational Background

PhD, Mathematics, University of Toronto, 2016
The equivariant geometry of nilpotent orbits and associated varieties
MS, Mathematics, University of Toronto, 2010
BS, Mathematics, Dalhousie University, 2009

Research Interests

My research harnesses techniques in Lie theory to elucidate structures arising at the interface of symplectic geometry and representation theory.

Publications | Journal Articles

Academic Journal

  • Crooks, P., Roeser, M., (2023). On the singularities of Mishchenko-Fomenko systems. Transformation Groups, 28, 1477-1494. doi:
  • Crooks, P., Weitsman, J., (2023). Abelianization and the Duistermaat-Heckman theorem. Bulletin of the London Mathematical Society
  • Crooks, P., Weitsman, J., (2023). The double Gelfand-Cetlin system, invariance of polarization, and the Peter-Weyl theorem. Journal of Geometry and Physics, 194
  • Crooks, P., Roeser, M., (2023). Hessenberg varieties and Poisson slices. Contemporary Mathematics of the AMS, 790, 25-57.
  • Crooks, P., Mayrand, M., (2022). Symplectic reduction along a submanifold. Compositio Mathematica, 158:9, 1878-1934.
  • Balibanu, A., Crooks, P., (2022). Perverse sheaves and the cohomology of regular Hessenberg varieties. Transformation Groups, doi:
  • Crooks, P., Roeser, M., (2022). The log symplectic geometry of Poisson slices. Journal of Symplectic Geometry, 20:1, 135-190.
  • Crooks, P., van Pruijssen, M., (2021). An application of spherical geometry to hyperkaehler slices. Canadian Journal of Mathematics, 73:3, 687-716.
  • Crooks, P., Weitsman, J., (2021). Towards a quantization of the double via the enhanced symplectic category. Research in the Mathematical Sciences, 8, 51pp.
  • Crooks, P., (2020). Kostant-Toda lattices and the universal centralizer. Journal of Geometry and Physics, 150, 16pp.
  • Crooks, P., Roeser, M., (2020). On the fibres of Mishchenko-Fomenko systems. Documenta Mathematica, 25, 1195-1239.
  • Crooks, P., Rayan, S., (2019). Abstract integrable systems on hyperkaehler manifolds arising from Slodowy slices. Mathematical Research Letters, 26:1, 9-33.
  • Crooks, P., (2019). Complex adjoint orbits in Lie theory and geometry. Expositiones Mathematicae, 37:2, 104–144.
  • Abe, H., Crooks, P., (2019). Hessenberg varieties, Slodowy slices, and integrable systems. Mathematische Zeitschrift, 291:3-4, 1093-1132.
  • Crooks, P., (2018). An equivariant description of certain holomorphic symplectic varieties. Bulletin of the Australian Mathematical Society, 97:2, 207–214.
  • Crooks, P., Holden, T., (2016). Generalized equivariant cohomology and stratifications. Canadian Mathematical Bulletin, 59:3, 483–496.
  • Abe, H., Crooks, P., (2016). Hessenberg varieties for the minimal nilpotent orbit. Pure and Applied Mathematics Quarterly, 12:2, 183-223.
  • Crooks, P., (2016). Properties of nilpotent orbit complexification. Journal of Generalized Lie Theory and ApplicationsS2, 6pp.
  • Crooks, P., Rayan, S., (2016). Some results on equivariant contact geometry for partial flag varieties. International Journal of Mathematics, 27:8, 13pp.
  • Crooks, P., (2015). The torus-equivariant cohomology of nilpotent orbits. Journal of Lie Theory, 25:4
  • Crooks, P., Milson, R., (2009). On projective equivalence of univariate polynomial subspaces. SIGMA. Symmetry, Integrability, and Geometry. Methods and Applications, 5

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

Publications | Other

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.


MATH 6350 - Multilinear Algebra and Matrix Theory II (Representation Theory II), Spring 2024
MATH 6340 - Multilinear Algebra and Matrix Theory I (Representation Theory I), Fall 2023
MATH 6120 - Differential Geometry, Spring 2023
MATH 4200 - Foundations of Analysis, Fall 2022

Graduate Students Mentored

Mitchell Pound, Mathematics & Statistics
Xiang Gao, Mathematics & Statistics