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I am a Zelevinsky Postdoctoral Fellow in the Department of Mathematics at Northeastern University. 

My research is concerned with the manifestations and implications of symmetry in algebra and geometry. I thereby study the geometry of complex algebraic varieties, with a view to elucidating structures in symplectic geometry, representation theory, integrable systems, and mathematical physics. Such varieties include algebraic groups, cotangent bundles, coadjoint orbits, flag varieties, Slodowy slices, Hessenberg varieties, Springer fibres, Mishchenko-Fomenko fibres, wonderful compactifications, and Toda lattices. My techniques are largely Lie-theoretic in nature, drawing from Kostant’s works on invariant theory, the Mishchenko-Fomenko approach to complete integrability, and the results of Goresky–Kottwitz–MacPherson on equivariant cohomology. For more information, please see my list of research papers.

For a brief overview of my academic background, please see my CV.

For a list of the courses I have taught, please see my teaching history.

I am helping to organize the seminars Geometry, Physics, and Representation Theory (GPRT) and Geometry, Algebra, Singularities, and Combinatorics (GASC), each of which is held at Northeastern University.

Alex Suciu and I are organizing Compactifications, configurations, and cohomology, a conference to be held October 22-24, 2021.

Jeremy Lane organized Lie theory and integrable systems in symplectic and Poisson geometry, an online conference held June 5-7, 2020.

I helped to organize The combinatorics and geometry of Jordan type and commuting varieties, a one-day online conference held on March 20, 2020.

You can contact me by the following means. 

E-Mail: p.crooks@northeastern.edu

Mailing Address:
Department of Mathematics 

Northeastern University 
567 Lake Hall 
Boston, MA 02115 
USA