Research
Leslie Hogben, Department of Mathematics, Iowa State University
The primary focus of my current research is in
combinatorial
matrix theory, specifically: 1) Minimum rank and spectral
properties
of fasmilies of matrices associated with a graph, digraph or sign
pattern. 2) Matrix completion problems
for patterns
of certain types of matrices, such as M-matrices, inverse M-matrices,
and
P-matrices, using graph theory.
I also work on stable and convergent matrices. A long time ago I
worked on Jordan and other nonassociative algebras and connections
between
ring theory and universal algebra. There is an active ISU
Discrete
Mathematics Seminar
meeting weekly during the academic year. I frequently lead the ISU Combinatorial Matrix Theory Research Group,
sometimes as an REU (research experiences for undergraduates) or EGR
(early graduate research) program.
Papers on minimum
rank of the family of symmetric matrices associated with a
graph or sign
pattern.
Catalogs of
graphs listing minimum rank (linked to this AIM page)
Subscriber
link to LAA web site
Universally
optimal matrices and field independence of the minimum rank of a graph (with DeAlba,
Grout, Mikkelson, Rasmussen) [PDF
preprint]
On the minimum rank of not necessarily symmetric matrices: A
preliminary study (AIM SQuaRE: Barioli, Fallat, Hall, Hershkowitz,
Hogben, van der Holst, Shader) [PDF
preprint]
Generic
maximum nullity of a graph (with Bryan Shader) [PDF
preprint]
An upper
bound for the minimum rank of a graph (with Berman, Friedland,
Rothblum, Shader) [PDF
preprint] To appear in Linear
Algebra and Its Applications.
Orthogonal
representations, minimum rank, and graph complements Linear Algebra and
Its
Applications, 428/11-12 (2008) pp 2560-2568. [PDF
preprint]
Zero forcing
sets and the minimum rank of graphs (AIM minimum rank -
special graphs work group, 18 authors) Linear Algebra and
Its
Applications, 428/7 (2008) 1628–1648. [PDF
preprint].
Minimum rank of matrices
described by a graph or pattern over the
rational, real and complex numbers (with Berman, Friedland,
Rothblum, Shader). Electronic Journal
of Combinatorics, 15/1 (2008) R 25
(19 pages). Appendix
The Minimum Rank of Symmetric
Matrices Described by a Graph: A
Survey (with
Shaun Fallat)
Linear Algebra and
Its
Applications, 426 (2007)
558-582. [PDF preprint
]
Minimum Rank
of a Tree over an Arbitrary Field (with Nathan L. Chenette,
Sean V. Droms, Rana Mikkelson and Olga Pryporova)
Electronic Journal of
Linear
Algebra 16 (2007): 183-186.
Forbidden Minors for
the Class of Graphs G with xi(G) <= 2 (with van der Holst) Linear Algebra and
Its
Applications 423 (2007) 42-52 [PDF preprint
].
Rational
Realization of Maximum Eigenvalue Multiplicity of Symmetric Tree Sign
Patterns (with Chowdhury, Melancon,
Mikkelson), Linear
Algebra and
Its
Applications 418 (2006)
380-393 pdf preprint.
Minimum Rank and Maximum
Eigenvalue
Multiplicity of Symmetric Tree Sign Patterns
(with
DeAlba, Hardy, Hentzel, Wangsness), Linear
Algebra and Its
Applications 418 (2006)
389-415 PDF preprint
A variant on
the graph
parameters
of Colin de Verdiere: Implications to the minimum rank of graphs
(with
Barioli, Fallat) Electronic
Journal of Linear Algebra 13
(2005), 387-404: [PDF
]
Spectral Graph Theory and
the
Inverse Eigenvalue Problem of a Graph Electronic
Journal of Linear Algebra 14 (2005): 12-31 [PDF
]
On the Difference between
Maximal
Multiplicity and Path Cover Number for Tree-like Graphs (with
Barioli and Fallat) Linear Algebra and Its
Applications, 409 (2005)
13-31[PDF
preprint]
Computation of Path Cover
Number
and Minimal Rank for Graphs (with
Barioli and Fallat)
Linear Algebra and Its Applications 392
(2004):289-303.
[PDF preprint]
Papers on Spectrally
Arbitrary Sign/nonzero Patterns
Subscriber
link to LAA web site
Spectrally Arbitrary Patterns:
Reducibility and the 2n Conjecture (with DeAlba,
Hentzel, McDonald, Mikkelson, Pryporova, Shader, Vander Meulen) Linear
Algebra and
Its
Applications, 423 (2007) 262-276. [PDF
preprint]
Papers on Matrix
Completion
Problems
Subscriber
link to LAA web site
The Q-Matrix
Completion
Problem (with DeAlba and Sarma)
[
PDF preprint]
The
Copositive Matrix
Completion
Problem: Unspecified Diagonal, Linear
Algebra and Its Applications 420 (2007) 160-162. [
PDF preprint]
On completion problems for
various classes of P-matrices
(with Bowers, Evers, Shaner, Snider, Wangsness) Linear
Algebra and Its Applications 413 (2006) 342-354 [ PDF preprint]
The Copositive Matrix
Completion
Problem (with Johnson and
Reams)
Linear Algebra and Its Applications 408
(2005) 207-211 [PDF
preprint ]
Relationships between the
Completion
Problems for Various Classes of Matrices
Proceedings
of the 2003 SIAM Conference on Applied Linear Algebra [
PDF ]
The (Weakly) Sign Symmetric
P-Matrix
Completion Problems (with
DeAlba, Hardy, Wangsness)
Electronic
Journal of Linear Algebra 10 (2003): 257-271 [
PDF ]
The Nonnegative P0
-Matrix Completion Problem ( with Choi, DeAlba, Kivunge,
Nordstrom,
Shedenhelm)
Electronic
Journal of Linear Algebra 10 (2003): 46-59 [
PDF ].
Matrix Completion Problems
for
Pairs of Related Classes of Matrices
Linear
Algebra and Its Applications
373
(2003): 13-29
[ PDF preprint ]
The P0-Matrix
Completion
Problem ( with Choi, DeAlba, Maxwell, Wangsness)
Electronic
Journal of Linear Algebra 9 (2002): 1-20 [
PDF].
The Symmetric M-Matrix and
Symmetric
Inverse M-Matrix Completion Problems
Linear Algebra
and Its Applications) 353 (2002):
159-167 [
PDF preprint ]
Graph Theoretic Methods for
Matrix
Completion Problems
Linear
Algebra and Its Applications 328 (2001):
161-202 [PDF preprint
]
Completions of P-Matrix
Patterns
(with Luz DeAlba)
Linear
Algebra and Its Applications 319 (2000): 83-102
[
PDF preprint ]
Inverse M-Matrix
Completions
of Patterns Omitting Some Diagonal Positions
Linear Algebra and Its Applications 313 (2000):
173-192.
Completions of Inverse
M-Matrix
Patterns
Linear Algebra and Its Applications
282
(1998): 145-160.
Completions of M-Matrix
Patterns
Linear Algebra and Its Applications 285
(1998): 143-152.
Papers on Stable and
Convergent
Matrices
Multiplicative Perturbations
of
Stable and Convergent Operators, (with
Bryan Cain, Luz M. DeAlba, and Charles R. Johnson)
Linear Algebra and Its Applications 268
(1998): 151-169.
Recent Talks
Minimum Rank Problems: Recent
Developments
15th International
Linear Algebra Society Comnference, Cancun, June 2008 PDF slides
Combinatorial Matrix
Theory and Spectral Graph Theory
International Conference
on Algebra and Related Topics (ICART 2008), Bangkok, May 2008 PDF slides
Combinatorial Matrix
Theory
School of Applied
Mathematics, University of Electronic Science and Technology of China,
Chengdu, November 2007 PDF slides
Minimum Rank
Combination of PDF slides from Haifa
Matrix Theory Conference,
April
2007 and 14 ILAS Conference Shangai,
July 2007
Minimum Rank: An Introduction
Carleton Summer
Mathematics Program, June
2007 PDF slides
Spectrally Arbitrary Patterns:
Reducibility and the 2n Conjecture
13th Annual ILAS Conference, July
2006 PDF slides
A variant on the graph
parameters
of Colin de Verdiere: Implications to the minimum rank of graphs
Aveiro Workshop on Graph Spectra, April 10, 2006 PDF slides
Matrix Completion Problems
Combinatorial Matrix Theory Special Session, AMS Central Section
Meeting, Linclon, NE, Oct. 21-23, 2005. pdf
slides
Minimum Rank and Maximum
Eigenvalue
Multiplicity of Symmetric Tree Sign Patterns and Trees
Rocky Mountain Discrete Math Days, Laramie, Wyoming, Aug. 1-2,
2005. pdf slides
Students
Ph. D.
Rana Mikkelson current
Olga Pryporova current
Amy Wangsness
2005
M. S.
Olga Ruff
2007
Sandra Nordstrom 2002
Daniel Carberry 1995
Rachel
Lamp
1990
Joyati Chakraborty 1985
Linear
Algebra & Spectral Graph Theory
Sites
Linear
Algebra
Conferences
- Pictures
from China July 2007: 2nd ICAC (Beijing, Xi'an) and 14th ILAS
(Shanghai)
- AIM
Workshop: Spectra of families of matrices described by graphs,
digraphs, and sign patterns, Oct. 23-27, 2006
- Pictures
from AIM
Workshop
- Special Session on
Combinatorial
Matrix Theory, AMS Sectional Meeting, Lincoln, NE, Oct. 21-23, 2005
- Minisymposium: Spectral
Properties
of Families of Matrices described by Patterns or Graphs at 12th ILAS
Conference,
Regina, June 26-29, 2005
- 12th
ILAS Conference, Regina, Canada, June 26-29, 2005
- Pictures from Directions In
Combinatorial
Matrix Theory
Workshop, BIRS, Banff, Canada, May 6-8, 2004
- Topics in Linear
Algebra Conference
ISU, Ames. IA, September 13-14, 2002
- Pictures from
Combinatorial Matrix
Theory
Conference,
Pohang, Korea, January 14-17, 2002
