- representation theory
- algebraic voting theory
- applied representation theory
Applied Representation Theory
The Applied Representation Theory Group
is an undergraduate research group here at Harvey Mudd College.
The current focus of the group is algebraic voting theory.
Linear rank tests of uniformity: Understanding inconsistent outcomes
and the construction of new tests (with
A. Bargagliotti), Journal of Nonparametric Statistics 24
(2012), no. 2, 481-495.
Cyclotomic polynomials, symmetric polynomials, and a generalization of
Euler's totient function (with J. Freed-Brown, M. Holden, and
M. Vrable), Mathematics Magazine 85 (2012), no. 1, 44-50.
Voting, the symmetric group,
and representation theory (with
Z. Daugherty, A. Eustis, and G. Minton), The American Mathematical
Monthly 116 (2009), no. 8, 667-687.
Borda meets Pascal (JSTOR) (with M. Jameson and G. Minton), Math Horizons
16 (2008), no. 1, 8-10, 21.
(with M. Koyama and D. Neel),
Journal of Combinatorial Mathematics and Combinatorial Computing
62 (2007), 35-43.
Spectral analysis of the Supreme Court
(with B. Lawson and D. Uminsky),
Mathematics Magazine 79 (2006), no. 5, 340-346.
Dead Heat: The 2006 Public Choice Society Election
(with S. Brams and M. Hansen),
Public Choice 128 (2006), no. 3-4, 361-366.
Reflections acting efficiently on a building, Forum Mathematicum 18 (2006), no. 3, 419-425.
The linear complexity of a graph
(with D. Neel),
Electronic Journal of Combinatorics 13 (2006), Research Paper 9, 19 pp. (electronic).
Rooted trees and iterated wreath products of cyclic groups
(with R. Orellana and D. Rockmore),
Advances in Applied Mathematics 33 (2004), no. 3, 531-547.
Computing isotypic projections with the Lanczos iteration
(with D. Maslen and D. Rockmore),
SIAM Journal on Matrix Analysis and Applications 25 (2004), no. 3,
Radon transforms and the finite general linear groups,
Forum Mathematicum 16 (2004), no. 1, 97-107.
Two quick combinatorial proofs
(with A. Benjamin),
College Mathematics Journal 33 (2002), no. 5, 406-408.
An eigenspace approach to decomposing representations of finite groups, Ph.D. thesis, Dartmouth College, 2001.
Papers Under Review or in Progress
Generalized Condorcet winners (with A. Myers, J. Townsend, S. Wolff,
and A. Wu), under review.
A unifying framework for teaching nonparametric statistical tests (with
A. Bargagliotti), under review.
Maximal length submodule projections in a complex group algebra (with
A. Bargagliotti), preprint.