Randall R Holmes
Professor
Department of Mathematics and Statistics
Auburn University, AL 36849
202 Parker Hall
334-844-6571
holmerr@auburn.edu
Courses
Spring 2013
MATH 2660
Topics in Linear Algebra
MATH 5320/6320
Intro to Abstract Algebra II
Past
MATH 1617
Honors Calculus I
MATH 5310/6310
Intro to Abstract Algebra I
MATH 5500/6500
Intro to Topology
MATH 7310
Algebra I
MATH 7330
Linear Representations of Finite Groups
MATH 8310
Homological Algebra I
MATH 8320
Homological Algebra II
Experience
Auburn University
Professor
(2007-present)
Auburn University
Associate Professor
(1994-2007)
Auburn University
Assistant Professor
(1989-94)
Yale University
J. W. Gibbs Instructor
(1987-89)
Education
Ph.D. Mathematics (1987), University of Illinois-Urbana, Advisor: Professor Michio Suzuki.
M.A. Mathematics (1982), University of Missouri-Columbia.
Three years of study in music composition (1978-81), University of Missouri-Columbia.
B.S. Education (Mathematics and Physics) (1978), University of Missouri-Columbia.
Selected publications
(Links are to preprints)
Orthogonal bases of Brauer symmetry classes of tensors for the dihedral group
(with A. Kodithuwakku),
Linear Multilinear Algebra
(2012), in press.
The coefficient coalgebra of a symmetrized tensor space
(with D. Turner),
Linear Multilinear Algebra
60
(4) (2012), 385—396.
Asymptotic behavior of Iwasawa and Cholesky iterations
(with H. Huang and T.-Y. Tam),
Linear Algebra and Its Applications
(2011), in press.
Population inertia and its sensitivity to changes in vital rates or initial conditions
(with D. N. Koons and J. B. Grand),
Ecology
88
(2007), 2857—2867.
Temporal and latitudinal variation in Northern Bobwhite population dynamics
(with T. H. Folk and J. B. Grand),
Population Ecology
49
(3) (2007), 211—219.
Group Representations
(with T.-Y. Tam), chapter in
CRC Handbook of Linear Algebra
(2006), 68-1—11.
Simple modules for the restricted Cartan type Lie algebras
(with C. Zhang),
Algebr. Represent. Theory
9
, no. 3 (2006), 285—307.
Numerical Range of the Derivation of an Induced Operator
(with C. K. Li and T.-Y. Tam),
J. Austral. Math. Soc. (Series A)
82
(3) (2005), 325—343.
Orthogonality of cosets relative to irreducible characters of finite groups
,
Linear Multilinear Algebra
52,
no. 2 (2004), 133—143.
A generalization of the Deutsch-Jozsa quantum algorithm
(with F. Texier),
Far East J. Math. Sci. (FJMS)
9,
no. 3 (2003), 319—326.
Some simple modules for the restricted Cartan-type Lie Algebras
(with C. Zhang),
J. Pure Appl. Algebra
173,
no. 2 (2002), 135—165.
Simple modules with character height at most one for the restricted Witt algebras
,
J. Algebra
237,
no. 2 (2001), 446—469.
Distance to the convex hull of an orbit under the action of a compact Lie group
(with T.-Y. Tam),
J. Austral. Math. Soc. Ser. A
66,
no. 3 (1999), 331—357.
Simple restricted modules for the restricted Hamiltonian algebra
,
J. Algebra
199,
no. 1 (1998), 229—261.
Orthogonal bases of symmetrized tensor spaces
,
Linear Multilinear Algebra
39,
no. 3 (1995), 241—243.
A duality proof of a theorem of P. Hill
,
Proc. Amer. Math. Soc.
123,
no. 2 (1995), 351—353.
Dimensions of the simple restricted modules for the restricted contact Lie algebra
,
J. Algebra
170,
no. 2 (1994), 504—525.
Cartan invariants for the restricted toral rank two contact Lie algebra
,
Indag. Math. (N.S.)
5,
no. 3 (1994), 291—305.
Block degeneracy and Cartan invariants for graded Lie algebras of Cartan type
(with D. Nakano),
J. Algebra
161,
no. 1 (1993), 155—170.
Symmetry classes of tensors associated with certain groups
(with T.-Y. Tam),
Linear Multilinear Algebra
32,
no. 1 (1992), 21—31.
An algorithm for the projective characters of finite Chevalley groups
,
Rocky Mountain J. Math.
22,
no. 2 (1992), 611—630.
Simple restricted modules for the restricted contact Lie algebras
,
Proc. Amer. Math. Soc.
116,
no. 2 (1992), 329—337.
Brauer-type reciprocity for a class of graded associative algebras
(with D. Nakano),
J. Algebra
144,
no. 1 (1991), 117—126.
Projective characters of finite Chevalley groups
,
J. Algebra
124,
no. 1(1989), 158—182.