Math Research

Research Publications (reverse chronological):

  1. With Darius Bayegan. A Giambelli formula for the S^1-equivariant cohomology of type A Peterson varieties. Accepted for publication in Involve.
  2. With Rebecca Goldin and Tara S. Holm,. Torsion in the full orbifold K-theory of abelian symplectic quotients. Geom. Dedicata (2011) doi: 10.1007/s10711-011-9604-1.
  3. With Julianna Tymoczko. A positive Monk formula in the S^1-equivariant cohomology of type A Peterson varieties. Proc. London Math. Soc. (2011) doi: 10.1112/plms/pdq038.
  4. With Greg Landweber and Reyer Sjamaar. Divided differences and the Weyl character formula in equivariant K-theory. Math. Res. Lett. Vol.17, No.3 (2010), 507--527.
  5. With Graeme Wilkin. Morse theory of the moment map for representations of quivers. Geom. Dedicata (2010) doi: doi:10.1007/s10711-010-9508-5.
  6. With Rebecca Goldin, Tara S. Holm,, and Takashi Kimura. The full orbifold K-theory of abelian symplectic quotients. J. of K-theory (2010) doi:10.1017/is010005021jkt118.
  7. With Paul Selick. Kirwan surjectivity in K-theory for Hamiltonian loop group quotients. Quart. J. of Math. (2008) doi:10.1093/qmath/han031.
  8. With Greg Landweber.The K-theory of abelian symplectic quotients. Math. Res. Lett. Vol. 15, No. 1 (2008), 57--72.
  9. With Rebecca Goldin. Orbifold cohomology of hypertoric varieties. Internat. J. Math. Vol. 19, No. 8 (2008), 1--30.
  10. With Greg Landweber. Surjectivity for Hamiltonian G-spaces in K-theory. Trans. Amer. Math. Soc. 359 (2007), 6001--6025.
  11. With Tara Holm, Lisa Jeffrey, and Augustin-Liviu Mare. Connectivity properties of moment maps for based loop groups. Geometry and Topology., Vol. 10 (2006), 1607--1634.
  12. The symplectic geometry of the Gel'fand-Cetlin-Molev basis for representations of Sp(2n,C). Journal of Sympl. Geom., Vol. 4, No. 1 (2006), pp. 1--41.
  13. With Andre Henriques and Tara Holm. Computation of generalized equivariant cohomologies of Kac-Moody flag varieties. This is a substantially revised and generalized version of the preprint below, "T-equivariant chomology of cell complexes and the case of infinite Grassmannians." Advances in Math. 197 (2005), 198--221.
  14. With Tara Holm. The equivariant cohomology of hypertoric varieties and their real loci. Comm. Anal. Geom, Vol. 13, No. 3 (2005), pp. 645--677.
  15. With Nicholas Proudfoot. Hyperpolygon spaces and their cores. Trans. Amer. Math. Soc., Vol. 357 (2005), pp. 1445--1467.
  16. With Nicholas Proudfoot. Properties of the residual circle action on a hypertoric variety. Pacific J. of Math, Vol. 214, No. 2 (2004), pp. 263--284.

Research Preprints (reverse chronological):

  1. With Barry Dewitt. Poset pinball, highest forms, and (n-2,2) Springer varieties. Submitted.
  2. With Darius Bayegan. Poset pinball, the dimension pair algorithm, and type A regular nilpotent Hessenberg varieties. Submitted.
  3. With Yael Karshon. Localization for equivariant cohomology with varying polarization. Submitted.
  4. With Julianna Tymoczko. Poset pinball, GKM-compatible subspaces, and Hessenberg varieties. Submitted.
  5. With Andre Henriques and Tara Holm. T-equivariant cohomology of cell complexes and the case of infinite Grassmannians.

Other publications:

  1. Toric Topology, Conference proceedings of the International Conference on Toric Topology, Osaka, May 2006. Editors: Megumi Harada, Yael Karshon, Mikiya Masuda, Taras Panov. Contemporary Mathematics, 460. American Mathematical Society, Providence, RI, 2008.