Research Interests

During the earlier part of my career, my research interests lay at the intersection of two fields: representation theory and combinatorics. Representation theory classifies the ways an algebraic object (such as a group, algebra, or Lie algebra) can act on a vector space. For groups and algebras related to Lie algebras, combinatorics plays an integral role in both stating and proving theorems about their representations. More recently, I have become interested in a slightly different mathematical intersection: graph theory and linear algebra.

Publications

"Power domination reconfiguration", (with B. Bjorkman, C. Bozeman, M. Flagg, D. Ferrero, L. Hogben, B. Jacob, and C. Reinhart) submitted.
"Minimum Rank with Zero Diagonal", (with J. Harmse, L. Hogben, T. Hunter, B. Jacob, A. Klimas, and S. McCathern) Elec. J. Lin. Alg, 27(2014), 2014, 458--477.
"The Rook Partition Algebra", J. Combin. Theory Ser. A, 113(2), 2006, 325--351.
"A Specht Module Analog for the Rook Monoid," E. J. Comb., 9 (1), 2002, R2.
Brauer Algebras and Centralizer Algebras for $SO(2n, C)$", J. Alg., 222 (1999), 678-707.