Peter Crooks

Publications | Books

• Crooks, P., Suciu, A., (2023). Compactifications, configurations, and cohomology. Contemporary Mathematics of the American Mathematical Society

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

Publications | Journal Articles

Academic Journal

• Crooks, P., Mayrand, M., (2026). Scheme-theoretic coisotropic reduction. Quarterly Journal of Mathematics, doi: https://doi.org/10.1093/qmath/haag005
• Crooks, P., (2026). Universal families of twisted cotangent bundles. Proceedings of the American Mathematical Society, 154:2, 863-881. doi: https://doi.org/10.1090/proc/17499
• Crooks, P., Gao, X., Pound, M., Thompson, C., (2025). Some incarnations of Hamiltonian reduction in symplectic geometry and geometric representation theory. Springer INDAM volume for "Poisson 2024"
• Crooks, P., Weitsman, J., (2024). Gelfand-Cetlin abelianizations of symplectic quotients. Pacific Journal of Mathematics, 333:2, 253-271. doi: 10.2140/pjm.2024.333.253
• Balibanu, A., Crooks, P., (2024). Perverse sheaves and the cohomology of regular Hessenberg varieties. Transformation Groups, 29:3, 909-933. doi: https://doi.org/10.1007/s00031-022-09755-3
• Crooks, P., Roeser, M., (2023). On the singularities of Mishchenko-Fomenko systems. Transformation Groups, 28, 1477-1494. doi: https://doi.org/10.1007/s00031-022-09718-8
• Crooks, P., Weitsman, J., (2023). Abelianization and the Duistermaat-Heckman theorem. Bulletin of the London Mathematical Society, 55:6, 2732-2742.
• 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.
• 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.