Math Research

Research Publications (reverse chronological):

  1. With Lisa C. Jeffrey and Paul Selick. The module structure of the equivariant K-theory of the based loop group of SU(2). Accepted for publication in Expositiones Math.
  2. With Lisa C. Jeffrey and Paul Selick. The product structure of the equivariant K-theory of the based loop group of SU(2). Accepted for publication in Quarterly J. of Math.
  3. With Yael Karshon. Localization for equivariant cohomology with varying polarization. Accepted for publication in Comm. Anal. Geom.
  4. With Darius Bayegan. Poset pinball, the dimension pair algorithm, and type A regular nilpotent Hessenberg varieties. ISRN Geometry, Volume 2012, Article ID: 254235 (2012), doi:10.5402/2012/254235.
  5. With Darius Bayegan. A Giambelli formula for the S^1-equivariant cohomology of type A Peterson varieties. Involve, Volume 5, Number 2 (2012), 115--132.
  6. With Barry Dewitt. Poset pinball, highest forms, and (n-2,2) Springer varieties. Elec. J. of Comb. Volume 19, Issue 1 (2012), #P56.
  7. With Rebecca Goldin and Tara S. Holm,. Torsion in the full orbifold K-theory of abelian symplectic quotients. Geom. Dedicata Volume 157, Issue 1 (2012), Page 187-204. (Erratum: In the discussion preceding Theorem 6.2 in the published version, we assert that the Bruhat cells on the flag variety give equivariant Darboux charts near a fixed point of the flag variety. This is false. In Example 6.4 we use this erroneous assertion to justify a calculation of the orbifold K-theory of a symplectic quotient of a flag variety of type B_3. Our calculation is still valid provided that the level set is chosen to be close enough to the fixed point. In addition, Proposition 2.8 of the paper The Gromov width of complex Grassmannians by Karshon and Tolman provides an equivariant Darboux chart which contains the level set as drawn in Figure 6.2. A corrected version of the paper is posted on the ArXiv.)
  8. With Julianna Tymoczko. A positive Monk formula in the S^1-equivariant cohomology of type A Peterson varieties. Proc. London Math. Soc. Vol. 103, No. 1 (2011), 40--72, doi: 10.1112/plms/pdq038.
  9. 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.
  10. With Graeme Wilkin. Morse theory of the moment map for representations of quivers. Geom. Dedicata Vol. 150, No. 1 (2011), 307--353.
  11. With Rebecca Goldin, Tara S. Holm,, and Takashi Kimura. The full orbifold K-theory of abelian symplectic quotients. J. of K-theory Vol. 8, Issue 02 (2011), 339-362.
  12. With Paul Selick. Kirwan surjectivity in K-theory for Hamiltonian loop group quotients. Quart. J. of Math. Vol. 61, Issue 1 (2008), 69--86, doi:10.1093/qmath/han031.
  13. With Greg Landweber.The K-theory of abelian symplectic quotients. Math. Res. Lett. Vol. 15, No. 1 (2008), 57--72.
  14. With Rebecca Goldin. Orbifold cohomology of hypertoric varieties. Internat. J. Math. Vol. 19, No. 8 (2008), 1--30.
  15. With Greg Landweber. Surjectivity for Hamiltonian G-spaces in K-theory. Trans. Amer. Math. Soc. 359 (2007), 6001--6025.
  16. 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.
  17. 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.
  18. 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.
  19. With Tara Holm. The equivariant cohomology of hypertoric varieties and their real loci. Comm. Anal. Geom, Vol. 13, No. 3 (2005), pp. 645--677.
  20. With Nicholas Proudfoot. Hyperpolygon spaces and their cores. Trans. Amer. Math. Soc., Vol. 357 (2005), pp. 1445--1467.
  21. 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 Derek Krepski. Global quotients among toric Deligne-Mumford stacks.
  2. With Kiumars Kaveh.. Integrable systems, toric degenerations and Okounkov bodies.
  3. With Julianna Tymoczko. Poset pinball, GKM-compatible subspaces, and Hessenberg varieties. Submitted.
  4. With Andre Henriques and Tara Holm. T-equivariant cohomology of cell complexes and the case of infinite Grassmannians.

Expository papers:

Other publications:

  • 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.