# Research

Those who are interested can read an essay I wrote for non-experts about one area of my research (support varieties for Lie superalgebras). For further details on my research activities please see my curriculum vita.

# Research Grants

In addition to the support I receive from the University of Oklahoma, I have been the Principal Investigator on the following research grants:

- American Institute of Mathematics Research SQuaRE (2020-2024)
- Simons Foundation Collaboration Grant (2017-2024)
- NSA Research Grant H98230-16-0055 (2016-2017)
- NSF Research Grant DMS-1160763 (2012-2016)
- NSF Conference Grant DMS-1406933 (2014)
- NSA Research Grant H98230-11-1-0127 (2011-2012)
- NSF Research Grant DMS-0734226 (2007-2011)
- NSF Postdoctoral Fellowship DMS-0402916 (2004-2007)

# Publications

- A survey of support theories for Lie superalgebras and finite supergroup schemes,

(with C. Drupieski),*submitted*, (2022). - Positivity and Web Bases for Specht Modules of Hecke Algebras,

(with S. Heard),*submitted*, (2022). - Support varieties for Lie superalgebras in characteristic 2,

(with C. Drupieski),*submitted*, (2022). - Howe
Duality of Type P,

(with N. Davidson and R. Muth),*submitted*, (2022). - Webs of Type P,

(with N. Davidson and R. Muth),*submitted*, (2022). - Quantum webs of type
Q,

(with N. Davidson and G. Brown),*submitted*. - Complexity and support varieties for type P Lie superalgebras,

(with B. Boe),*Math. Res. Lett.*,*to appear*. - Troesch complexes and cohomology for strict polynomial superfunctors,

(with C. Drupieski),*J. Pure Appl. Algebra*, 226, no 12, (2022). - Support varieties and modules of finite projective dimension for modular Lie superalgebras,

(with C. Drupieski, Appendix by S. Iyengar and L. Avramov),*Algebra & Number Theory*, 15, no. 5, (2021). - M-traces in
(non-unimodular) pivotal categories,

(with N. Geer and B. Patureau-Mirand),*Algebras Represent. Theory*,*to appear*. - Support schemes
for infinitesimal unipotent supergroups,

(with C. Drupieski),*Advances in Math.*, 384, (2021). - Webs of type
Q,

(with G. Brown),*Algebraic Combin.*, Volume 4, (2021). - On the
cohomological spectrum and support varieties for infinitesimal
unipotent supergroup schemes,

(with C. Drupieski),*Advances in Algebra*, Springer Proc. Math. Stat., vol. 277, Springer, (2019), pp. 121-167. - Graded
analogues of one-parameter subgroups and applications to the
cohomology of GL_{m|n(r)},

(with C. Drupieski),*Advances in Math.*, Volume 348, (2019), 228-277. - On support varieties
for Lie superalgebras and finite supergroup schemes,

(with C. Drupieski),*J. of Algebra*, Volume 525, (2019), 64-110. - A basis
theorem for degenerate affine Brauer-Clifford
supercategories,

(with J. Brundan and J. Comes),*Canadian J. of Math*, Volume 71, (2019), 1061-1101. - Geometric Schur duality
of classical type,

(with H. Bao, Y. Li, W. Wang),*Transformation Groups*, Volume 23, (2018), 329-389. - Tensor triangulated geometry
for classical Lie superalgebras,

(with B. Boe and D. Nakano),*Advances in Math.*, Volume 314, (2017), 228-277. - The marked Brauer
category,

(with B. Tharp),*J. London Math. Soc.*, Volume 95, (2017), No. 2, 393-413. - Presenting
Schur superalgebras

(with H. El Turkey),*Pacific J. Math.*, Volume 262, (2013), No. 2, 285-316. - Ambidextrous
objects and trace functions for
nonsemisimple
categories

(with N. Geer and B. Patureau-Mirand),*Proc. Amer. Math. Soc.*, Volume 141, (2013), no. 9, 2963-2978. - The
generalized Kac-Wakimoto
conjecture and support varieties for the Lie superalgebra
osp(m|2n),

*SE Lie Theory Conf. Proc., Proc. Symp. Pure Math.*, Volume 86, (2012). - Modified
traces on Deligne's category
Rep(S_t)

(with J. Comes),*J. Algebraic Combin.*, Volume 36, no. 4, (2012), 541-560. -
Complexity for modules over
the classical Lie superalgebra
gl(m|n)

(with B. Boe and D. Nakano),*Compositio Math.*, Volume 148, Issue 5, (2012), 1561-1592. - Degenerate affine Hecke-Clifford algebras and type Q Lie superalgebras

(with D. Hill and J. Sussan),*Math. Zeit.*, Volume 268, Numbers 3-4 (2011), 1091-1158. - Generalized trace and modified dimension functions on ribbon categories

(with N. Geer and B. Patureau-Mirand),*Selecta Math.*, Volume 17, Issue 2 (2011), 453-504. - Complexity and module varieties for classical Lie superalgebras

(with B. Boe and D. Nakano),*Int. Math. Res. Not.*, IMRN 2011, no. 3, 696-724. - Cohomology and support varieties for Lie superalgebras

(with B. Boe and D. Nakano),*Trans. Amer. Math. Soc.*,**362**(2010), 6551-6590. - Cohomology and support varieties for Lie superalgebras, II

(with B. Boe and D. Nakano),*Proc. London Math. Soc.*,**98**(2009), no. 1, 19-44. - On Kostant's theorem for Lie algebra cohomology

(with UGA VIGRE Algebra Group),*Cont. Math.***478**(2009) 39-60. - Cohomology and support varieties for the Lie superalgebra W(n)

(with I. Bagci and D. Nakano),*Int. Math. Res. Not.*IMRN 2008, Art. ID rnn115, 42 pp. - Support varieties for Weyl modules over bad primes

(with UGA VIGRE Algebra Group),*J. Algebra*,**312**(2007), no 2., 602-633. - The Steinberg tensor product theorem for GL(m|n)
*Cont. Math.***413**(2006), 123-132. - Representation type of Schur superalgebras

(with D. Hemmer and D. Nakano),*J. Group Theory***9**(2006), no 3., 283-306. - Crystal structures arising from representations of GL(m|n)
*Represent. Theory***10**(2006), 49-85. - Varieties of nilpotent elements for simple Lie algebras II: bad primes

(with UGA VIGRE Algebra Group),*J. Algebra***292**no 1. (2005), 65-99. - A new proof of the Mullineux conjecture

(with J. Brundan),*J. Algebraic Combin.***18**no 1. (2003), 13-39.