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)
  • Simons Foundation Collaboration Grant (2017-2022)
  • 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

  1. Complexity and support varieties for type P Lie superalgebras,
    (with B. Boe), submitted.
  2. Quantum webs of type Q,
    (with N. Davidson and G. Brown), submitted.
  3. Support varieties and modules of finite projective dimension for modular Lie superalgebras,
    (with C. Drupieski, Appendix by S. Iyengar and L. Avramov), submitted.
  4. M-traces in (non-unimodular) pivotal categories,
    (with N. Geer and B. Patureau-Mirand), submitted.
  5. Support schemes for infinitesimal unipotent supergroups,
    (with C. Drupieski), submitted.
  6. Webs of type Q,
    (with G. Brown), submitted.
  7. Tensor triangulated geometry for quantum groups,
    (with B. Boe and D. Nakano), submitted.
  8. 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.
  9. 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.
  10. On support varieties for Lie superalgebras and finite supergroup schemes,
    (with C. Drupieski), J. of Algebra, Volume 525, (2019), 64-110.
  11. A basis theorem for degenerate affine Brauer-Clifford supercategories,
    (with J. Brundan and J. Comes), Canadian J. of Math, Volume 71, (2019), 1061-1101.
  12. Geometric Schur duality of classical type,
    (with H. Bao, Y. Li, W. Wang), Transformation Groups, Volume 23, (2018), 329-389.
  13. Tensor triangulated geometry for classical Lie superalgebras,
    (with B. Boe and D. Nakano), Advances in Math., Volume 314, (2017), 228-277.
  14. The marked Brauer category,
    (with B. Tharp), J. London Math. Soc., Volume 95, (2017), No. 2, 393-413.
  15. Presenting Schur superalgebras
    (with H. El Turkey), Pacific J. Math., Volume 262, (2013), No. 2, 285-316.
  16. 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.
  17. 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).
  18. Modified traces on Deligne's category Rep(S_t)
    (with J. Comes), J. Algebraic Combin., Volume 36, no. 4, (2012), 541-560.
  19. 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.
  20. 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.
  21. 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.
  22. Complexity and module varieties for classical Lie superalgebras
    (with B. Boe and D. Nakano), Int. Math. Res. Not., IMRN 2011, no. 3, 696-724.
  23. Cohomology and support varieties for Lie superalgebras
    (with B. Boe and D. Nakano), Trans. Amer. Math. Soc., 362 (2010), 6551-6590.
  24. Cohomology and support varieties for Lie superalgebras, II
    (with B. Boe and D. Nakano), Proc. London Math. Soc., 98 (2009), no. 1, 19-44.
  25. On Kostant's theorem for Lie algebra cohomology
    (with UGA VIGRE Algebra Group), Cont. Math. 478 (2009) 39-60.
  26. 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.
  27. Support varieties for Weyl modules over bad primes
    (with UGA VIGRE Algebra Group), J. Algebra, 312 (2007), no 2., 602-633.
  28. The Steinberg tensor product theorem for GL(m|n)
    Cont. Math. 413 (2006), 123-132.
  29. Representation type of Schur superalgebras
    (with D. Hemmer and D. Nakano), J. Group Theory 9 (2006), no 3., 283-306.
  30. Crystal structures arising from representations of GL(m|n)
    Represent. Theory 10 (2006), 49-85.
  31. Varieties of nilpotent elements for simple Lie algebras II: bad primes
    (with UGA VIGRE Algebra Group), J. Algebra 292 no 1. (2005), 65-99.
  32. A new proof of the Mullineux conjecture
    (with J. Brundan), J. Algebraic Combin. 18 no 1. (2003), 13-39.