Summary
I work in the general area of algebraic combinatorics, and the more specific subarea of combinatorial representation theory. Here, the general idea is to study algebraic structures via the combinatorics of their actions on modules.
My favorite structures to study are groups of Lie type—especially unipotent ones—Hecke algebras, and diagram algebras. I find the notion of supered representation theories especially compelling as a tool to extract maximal combinatorial and Hopf theoretic structure, and have devoted a fair amount of effort in this direction.
Please let me know if you are interested in talking in the Algebraic Lie Theory Seminar, which I coorganize with Tianyuan Xu and Richard Green.
Preprints and papers
With F. Aliniaeifard, Hopf structures in the representation theory of direct products, (2021) submitted.
With F. Aliniaeifard, A categorification of the Malvenuto–Reutenauer algebra via a tower of groups, Adv. Math. 383 (2021), 107675.
With F. Aliniaeifard, The structure of normal lattice supercharacter theories, Algebraic Combinatorics 3 (2020), 10591078.
With F. Aliniaeifard, Pattern groups and a poset based Hopf monoid, J. Comb. Theory Ser. A 172 (2020), 31 pages.
Supercharacter theories of type A unipotent radicals and unipotent polytopes, Algebraic Combinatorics 1 (2018), 2345.
With S. Andrews, The combinatorics of GL_{n} generalized GelfandGraev characters, J. London Math. Soc. 95 (2017), 475499.
With D. Bragg, Poset binomial coefficients and restrictions of supercharacters, J. Algebra 451 (2016), 357400.
With D. BakerJarvis and N. Bergeron, Antipode and primitive elements in the Hopf monoid of supercharacters, J. Algebraic Combin. 40 (2014), 903938.

With M. Aguiar and N. Bergeron, Hopf monoids from class functions on unitriangular matrices, Algebra Number Theory 7 (2013), 17431779.

With N. Bergeron, A supercharacter table decomposition via powersum symmetric functions, Internat. J. Algebra Comput. 23 (2013), 763778.

With S. Fu, V. Reiner, and D. Stanton, The negative qbinomial, Electr. J. Combin. 19(1) P36 (2012), 24 pages.

With M. Aguiar, C. Andre, C. Benedetti, N. Bergeron, Z. Chen, P. Diaconis, A. Hendrickson, S. Hsiao, I. M. Isaacs, A. Jedwab, K. Johnson, G. Karaali, A. Lauve, T. Le, S. Lewis, H. Li, K. Magaard, E. Marberg, JC. Novelli, A. Pang, F. Saliola, L. Tevlin, JY. Thibon, V. Venkateswaran,C.R. Vinroot, N. Yan, M. Zabrocki, Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras, Adv. Math. 229 (2012), 23102337.

With S. Lewis, Nonzero coefficients in restrictions and tensor products of supercharacters of U_{n}(q), Adv. Math. 227 (2011), 4072.

With T. Halverson, qPartition Algebra Combinatorics, J. Combin. Theory Ser. A 117 (2010), 507527.

Branching rules in the ring of superclass functions of unipotent uppertriangular matrices. J. Algebraic Combin. 31 (2010), 267298.

With E. Marberg, Superinduction for pattern groups, J. Algebra 321 (2009), 36813703.

With V. Venkateswaran, Restricting supercharacters of the finite group of unipotent uppertriangular matrices, Electron. J. Combin. 16(1) Research paper 23 (2009), 32 pages.

With C.R. Vinroot, GelfandGraev characters of the finite unitary groups, Electron. J. Combin. 16(1) Research Paper 146 (2009), 37 pages.

With P. Diaconis, Supercharacter formulas for pattern groups, Trans. Amer. Math. Soc. 361 (2009), 35013533.

With C.R. Vinroot, Values of characters sums for finite unitary groups, J. Algebra 320 (2008), 11501173.

With C.R. Vinroot, On the characteristic map of finite unitary groups, Adv. Math. 210 (2007), 707732.

A skeinlike multiplication algorithm for unipotent Hecke algebras, Trans. Amer. Math. Soc. 359 (2007), 16851724.

Unipotent Hecke algebras of GL_{n}(F_{q}), J. Algebra 284 (2005), 559577.

Unipotent Hecke algebras: the structure, representation theory and combinatorics, Ph.D Thesis (2004).

With J. Swallow, Quadratic Corestriction, C_{2}embedding problems, and explicit construction, Comm. in Algebra 30 (2002), 32273258.