Math Research

Peer-Reviewed Research Publications (reverse chronological):

1. With B\"usra Atar, Kieran Bhaskara, Adrian Cook, Sergio Da Silva, Jenna Rajchgot, Adam Van Tuyl, Runyue Wang, Jay Yang. Hadamard products and binomial ideals. Electronic preprint, 2022, available on the ArXiv.
2. With Sergio Da Silva. Geometric vertex decomposition, Groebner bases, and Frobenius splittings for regular nilpotent Hessenberg varieties. Electronic preprint, 2022, available on the ArXiv. Accepted in 2023 for publication in Transformation Groups.
3. With Martha Precup. Torus fixed point sets of Hessenberg Schubert varieties in regular semisimple Hessenberg varieties. Osaka J. Math. Volume 60 (2023), No. 3, 637--652.
4. With Jeremy Lane and Aidan Patterson. A local normal form for Hamiltonian actions of compact semisimple Poisson-Lie groups. Involve, a Journal of Mathematics Volume 15-5 (2022), 775--812. DOI: 10.2140/involve.2022.15.775.
5. With Martha Precup. Upper-triangular linear relations on multiplicities and the Stanley-Stembridge conjecture. Electronic Journal of Combinatorics Volume 29 (2022) Issue 3, P3.16.
6. With Maryam Nowroozi and Adam Van Tuyl. Virtual resolutions of points in P1 x P1. Journal of Pure and Applied Mathematics Volume 226 (2022) 107140.
7. With Martha Precup and Julianna Tymoczko. Toward permutation bases in the equivariant cohomology rings of regular semisimple Hessenberg varieties. La Matematica Volume 1 (2022) 263?316.
8. With Laura Escobar. Wall-crossing for Newton-Okounkov bodies and the tropical Grassmannian. Internat. Math. Res. Notices Volume 2022 (2022) Issue 7, 5152?5203.
9. With Tatsuya Horiguchi and Satoshi Murai and Martha Precup and Julianna Tymoczko. A filtration on the cohomology rings of regular nilpotent Hessenberg varieties. Mathematische Zeitschrift Volume 298, no. 3 (2021), 1345--1382.
10. With Kiumars Kaveh and Mark Hamilton. Convergence of polarizations, toric degenerations, and Newton-Okounkov bodies. Comm. Anal. Geom. Volume 29, no. 5 (2021), 1183--1231.
11. With Martha Precup. The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture. J. of Algebraic Combinatorics Volume 2, no. 6 (2019), 1059--1108.
12. With Tatsuya Horiguchi and Mikiya Masuda and Seonjeong Park. The volume polynomial of regular semisimple Hessenberg varieties and the Gelfand-Zetlin polytope. Proceedings of the Steklov Institute of Mathematics, Vol. 305, Issue 1 (2019), 318-344.
13. With Martha Precup. Upper-triangular linear relations on multiplicities and the Stanley-Stembridge conjecture. Electronic preprint, 2018, available on ArXiv.
14. With Jihyeon Jessie Yang. Singular string polytopes and functorial resolutions from Newton-Okounkov bodies. Illinois J. Math. Vol. 62, No.1-4 (2018), 271--292.
15. With Hiraku Abe, Lauren DeDieu, and Federico Galetto. Geometry of Hessenberg varieties with applications to Newton-Okounkov bodies. Selecta Math. New Ser. Vol. 24, Issue 3 (2018) 2129--2163. NOTE: The published version contains minor errors in Section 3.5 and Sections 6 and 7. The most recent ArXiv version corrects these errors. The main results are unaffected by the errors.
16. With Hiraku Abe, Tatsuya Horiguchi, and Mikiya Masuda. The cohomology rings of regular nilpotent Hessenberg varieties in Lie type A. Int. Math. Res. Notices Vol. 2017, no. 0000 (2017) 1--73.
17. With Julianna Tymoczko. Poset pinball, GKM-compatible subspaces, and Hessenberg varieties. J. of the Math. Soc. of Japan Vol. 69, No. 3 (2017), 945--994
18. With Jihyeon Jessie Yang. Newton-Okounkov bodies of Bott-Samelson varieties and Grossberg-Karshon twisted cubes. Michigan Math. J. Vol. 65, Issue 2 (2016), 413--440.
19. With Tara Holm, Nigel Ray and Gareth Williams.The equivariant $K$-theory and cobordism rings of divisive weighted projective spaces. Tohoku J. of Math. (2), Vol. 68, No. 4 (2016), 487--513.
20. With Rebecca Goldin, David Johannsen and Derek Krepski. Inertia groups of a toric DM stack, fake weighted projective spaces, and labelled sheared simplices. Rocky Mt. J. of Math. Vol. 46, No. 2 (2016), 481--517.
21. With Jihyeon Jessie Yang. Grossberg-Karshon twisted cubes and basepoint-free divisors. J. of Korean Math. Soc. Vol. 52 (2015), no. 4, 853--868.
22. With Eunjeong Lee. Grossberg-Karshon twisted cubes and hesitant walk avoidance. Pacific J. of Math. Vol. 278 (2015), no. 1, 119--136.
23. With Tatsuya Horiguchi and Mikiya Masuda. The equivariant cohomology rings of Peterson varieties in all Lie types. Can. Bull. Math., Vol. 58 (2015), 80-90.
24. With Yukiko Fukukawa and Mikiya Masuda. The equivariant cohomology rings of Peterson varieties. J. of the Math. Soc. of Japan., Vol. 67 (2015), no. 3, 1147--1159.
25. With Kiumars Kaveh.. Integrable systems, toric degenerations and Okounkov bodies. Inventiones Mathematicae. Vol. 202 (2015), no. 3, 927--985. DOI: 10.1007/s00222-014-0574-4.
26. With Derek Krepski. Global quotients among toric Deligne-Mumford stacks. Osaka J. of Math. Vol. 52 (2015), pp. 237--269.
27. With Hiraku Abe and Tatsuya Horiguchi and Mikiya Masuda. The equivariant cohomology rings of regular nilpotent Hessenberg varieties in Lie type A: research announcement. MORFISMOS (special volume in honor of Samuel Gitler), Vol. 18, no. 2 (2014), 51--65.
28. With Lisa C. Jeffrey and Paul Selick. The module structure of the equivariant K-theory of the based loop group of SU(2). Expositiones Math. Volume 32, Issue 1 (2014), pp. 1--32.
29. With Lisa C. Jeffrey and Paul Selick. The product structure of the equivariant K-theory of the based loop group of SU(2). Quarterly J. of Math. (2013) DOI: 10.1093/qmath/hat010.
30. With Yael Karshon. Localization for equivariant cohomology with varying polarization. Comm. Anal. Geom. 20 (2012), no.5, 869-947.
31. 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.
32. 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.
33. With Barry Dewitt. Poset pinball, highest forms, and (n-2,2) Springer varieties. Elec. J. of Comb. Volume 19, Issue 1 (2012), #P56.
34. 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.)
35. 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.
36. 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.
37. With Graeme Wilkin. Morse theory of the moment map for representations of quivers. Geom. Dedicata Vol. 150, No. 1 (2011), 307--353.
38. 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.
39. 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.
40. With Greg Landweber.The K-theory of abelian symplectic quotients. Math. Res. Lett. Vol. 15, No. 1 (2008), 57--72.
41. With Rebecca Goldin. Orbifold cohomology of hypertoric varieties. Internat. J. Math. Vol. 19, No. 8 (2008), 1--30.
42. With Greg Landweber. Surjectivity for Hamiltonian G-spaces in K-theory. Trans. Amer. Math. Soc. 359 (2007), 6001--6025.
43. 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.
44. 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.
45. 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.
46. With Tara Holm. The equivariant cohomology of hypertoric varieties and their real loci. Comm. Anal. Geom, Vol. 13, No. 3 (2005), pp. 645--677.
47. With Nicholas Proudfoot. Hyperpolygon spaces and their cores. Trans. Amer. Math. Soc., Vol. 357 (2005), pp. 1445--1467.
48. 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.