Research page

Graduate student supervision

Molly Fenn (PhD 2008), Teaching Professor, NC State.
Garret Cahill (Masters 2008), Lecturer, UMass Amherst.
Jennifer Koonz (PhD 2013), Intersystems, Cambridge, MA.
Ben Johnson (PhD 2017), Postdoctoral Fellow, Oklahoma State (first job).

Postdoctoral mentoring

Ralf Schiffler, UConn
Theo Douvropoulos, Brandeis (co-mentored with Alejandro Morales)
Chengze Duan, currently, (co-mentored with Alexei Oblomkov)

Papers

Automorphisms and deformations of regular semisimple Hessenberg varieties (with Patrick Brosnan, Laura Escobar, Jaehyun Hong, Donggun Lee, Eunjeong Lee, and Anton Mellit), 48 pages, 2024.
Constructible representations and Catalan numbers (with George Lusztig), 10 pages, 2024, accepted in the Pacific Journal of Math (special issue in memory of Gary Seitz).
Minimal special degenerations and duality (with Daniel Juteau and Paul Levy), 40 pages, 2023.
Local geometry of special pieces of nilpotent orbits (with Baohua Fu, Daniel Juteau, and Paul Levy), 37 pages, 2023.
Perverse sheaves, nilpotent Hessenberg varieties, and the modular law (with Martha Precup), 27 pages, 2022, accepted in the Pure and Applied Mathematics Quarterly (special volume for George Lusztig).
A new family of isolated symplectic singularities with trivial local fundamental group (with Gwyn Bellamy, Cédric Bonnafé, Baohua Fu, Daniel Juteau, and Paul Levy), 22 pages, 2021, accepted in Proceedings of the LMS.
A transitivity result for ad-nilpotent ideals in type A (with Molly Fenn), Indagationes Mathematicae, Vol 32, Issue 6, 2021, 1175--1189 (Memorial volume for T. Springer).
Invariant theory for coincidental complex reflection groups (with Vic Reiner and Anne Shepler), Mathematische Zeitschrift, 2020.
Equations for some nilpotent varieties (with Ben Johnson), IMRN, Volume 2020, Issue 14, July 2020, Pages 4433–4464 (online publication July 2018).
Irreducible local systems on nilpotent orbits, Vol 13, No. 3, Bulletin of the Institute of Mathematics Academia Sinica (New Series), 2018.
Weyl group q-Kreweras numbers and cyclic sieving (with Vic Reiner),
Annals of Combinatorics Volume 22, Issue 4, pp 819–874 (2018).
Generic singularities of nilpotent orbit closures (with Baohua Fu, Daniel Juteau, and Paul Levy)
Advances in Mathematics 305, (2017), 1--77.
Appendix B in Representations of semisimple Lie algebras in prime characteristic and noncommutative Springer resolution by Roman Bezrukavnikov and Ivan Mirkovic (2013).
Exterior powers of the reflection representation in Springer theory
Transformation Groups 16 (2011), no. 3, 889--911 (volume in honor of Tonny Springer).
Pieces of nilpotent cones for classical groups (with Pramod Achar and Anthony Henderson)
Representation Theory 15 (2011), 584-616.
Cohomology of line bundles on the cotangent bundle of a Grassmannian
Proceedings of the AMS 137 (2009), no. 10, 3291--3296.
Equivalence classes of B-stable ideals
Nagoya Journal of Mathematics, Vol. 183 (2006), 161--184 (volume in honor of George Lusztig).
Exponents for B-stable ideals (with Julianna Tymoczko), version of June 2004.
Transactions of the AMS, 358, (2006), no. 8, 3493--3509.
Normality of very even nilpotent varieties in D_2l , version of January 2004.
Bulletin London Math. Soc., 37, (2005), no. 3, 351--360.
B-stable ideals in the nilradical of a Borel subalgebra, version of October 2003.
Canadian Math Bulletin, 48, (2005), no. 3, 460--472.
A characterization of Dynkin elements (with Paul Gunnells)
Math Research Letters 10, (2003), no. 2-3, 363--373.
Normality of nilpotent varieties in E_6
Journal of Algebra, 270 (2003), no. 1, 288-306.
Component groups of unipotent centralizers in good characteristic (with George McNinch)
Issue celebrating the 80th birthday of Robert Steinberg, J. Algebra, 260 (2003), no. 1, 323--337.
Local systems on nilpotent orbits and weighted Dynkin diagrams (with Pramod Achar)
Representation Theory, 6 (2002), 190--201.
Lusztig's canonical quotient and generalized duality
Journal of Algebra, Vol. 243 (2001), 790-812.
Conjectures for small representations of the exceptional groups
Comm. Math. Univ. Sancti Pauli, Vol. 49 (2000), No. 1, 101-104.
A generalization of the Bala-Carter theorem
IMRN (1998), 539-562.
The adjoint representation in rings of functions (with Peter Trapa)
Electronic Journal of Representation Theory, Vol. 1 (1997), 182-189.
A family of affine Weyl group representations
Transformation Groups, Vol. 2 (1997), No. 4, 375-390.
The homology of the space of affine flags containing a nilpotent element
Proceedings of the American Mathematical Society, Vol. 125 (1997), No. 8, 2481-2484.