This is a group of faculty and students who are interested in combinatorial matrix theory, with some or all of the research taking place at ISU. At the beginning of a session we begin by discussing the necessary background, such as the use of graphs and digraphs to study matrices and the use of matrices to study (di)graphs, and review recent developments. We then select a problem and begin active research. This is a great opportunity for graduate and undergraduate students to become involved in research-- past groups have published 20 papers with more under review Graduate linear algebra (Math 510) is a prerequisite for graduate students; undergraduate linear algebra (Math 317 or equivalent) is a prerequisite for the summer REU undergraduates and a course in graph theory is helpful. Post-doctoral associates and faculty at nearby colleges and universities are also welcome. Students often join at the beginning of spring semester for EGR (Math 610 Early Graduate Research), which will be offered in spring 2014, or at the beginning of the summer for the REU (Research Experiences for Undergraduates) sessions. The group used to meet starting at the beginning of each academic year. For more information contact Leslie Hogben.

- Leslie Hogben
- Michael Young
- Minerva Catral, Xavier U
- Adam Berliner, St. Olaf College
- Brenda Kroschel, U St Thomas

- Nicole Kingsley
- C-H Lin
- Chassidy Bozeman
- Andrew Smith

- Luz DeAlba (Drake U emeritus)
- Craig Erickson (Grand View U, Fall 2014)

- Nathan Warnberg (UW-LaCross, Fal 2014)

- Steven Osborne (webfilings)

- Geoff Tims, PhD 2013 (Nationwide Insurance)

- Travis Peters, PhD 2012, (Culver-Stockton College)
- Arianne Ross, MS 2011 (Coastal Carolina University)

- Darren Row, PhD 2011, (Upper Iowa University)

- Kaela Rasmusson (BS Honors, 2010)
- Jason Grout (Drake U, ISU postdoc 2007-9)
- Olga Pryporova Kurth (PhD 2009, postdoc, U Connecticut)
- Laura DeLoss (MS 2009)
- Rana Mikkelson (PhD 2008, US government)
- Amy Wangsness Wehe (Fitchburg State)

**2. The Nonnegative P_0-Matrix
Completion
Problem** (2001-2)

Choi, DeAlba, Hogben, Kivunge,
Nordstrom, Shedenhelm

*Electronic
Journal of Linear Algebra*** 10** (2003): 46-59

**3. The (Weakly) Sign Symmetric
P-Matrix
Completion Problems** (2002-3)

DeAlba, Hardy, Hogben, Wangsness

*Electronic
Journal of Linear Algebra*** 10** (2003): 257-271

**4. On completion problems for
various
classes of P-matrices **(2003 & 2004 REUs)
** **

Bowers, Evers,
Hogben, Shaner, Snider, Wangsness

*Linear
Algebra and Its Applications*
413 (2006) 342-354. [
PDF preprint ]

**5. Minimum Rank and Maximum
Eigenvalue
Multiplicity of Symmetric Tree Sign Patterns **(2004-5)

DeAlba,
Hardy, Hentzel, Hogben, Wangsness

*Linear
Algebra and Its
Applications *418 (2006)
389-415 pdf
preprint.

**6. Rational Realization of
Maximum
Eigenvalue Multiplicity of Symmetric Tree Sign Patterns **(2005 REU)
** **

Chowdhury,
Hogben, Melancon, Mikkelson

*Linear
Algebra and
Its
Applications *418 (2006)
380-393*,* pdf preprint.

**7. Spectrally Arbitrary Patterns: Reducibility and the 2n Conjecture **(2005-6)

DeAlba, Hentzel, Hogben, McDonald, Mikkelson, Pryporova, Shader, Vander Meulen

DeAlba, Grout, Hogben, Mikkelson, Rasmussen

**10. Minimum rank of skew-symmetric matrices described by a graph **(2008 IMA graduate summer program)

Allison, Bodine, DeAlba, Debnath, DeLoss, Garnett, Grout,
Hogben, Im, Kim, Nair, Pryporova, Savage, Shader,
Wangsness. Linear Algebra and its Applications 432 (2010) 2457–2472.

**11. Techniques
for determining the minimum rank of a small graph **** **(2008 EGR)

DeLoss,
Grout, Hogben, McKay, Smith, Tims

Linear Algebra and its Applications 432 (2010) 2995–3001. [PDF
preprint]

12. Minimum rank of certain families of graphs** **** **(2009 REU)

Almodovar, DeLoss, Hogben, Hogenson, Murphy, Peters, Ramirez. Involve: a journal of mathematics 3 (2010): 371-392. [PDF preprint]

*
*

Edholm, Hogben, Huynh, LaGrange, Row. Linear Algebra and its Applications 436 (2012): 4352–4372 [PDF preprint]

Archer, Catral, Erickson, Haber, Hogben, Martinez-Rivera, Ochoa. Involve 4 (2011): 405-410. PDF preprint

**15. Potentially eventually exponentially positive sign patterns **** **** **(2010 REU)

Archer, Catral, Erickson, Haber, Hogben, Martinez-Rivera, Ochoa. Involve 6 (2013): 261-271.

16. Note on positive semidefinite maximum nullity and positive semidefinite zero forcing number of partial 2-trees. (2011 EGR)

Ekstrand, Erickson, Hay, Hogben, Roat. Electonic Journal of Linear Algebra 23 (2012) 79-87 [PDF preprint]

Ekstrand, Erickson, Hall, Hay, Johnson, Kingsley, Osborne, Peters, Roat, Ross, Row, Warnberg, Young. Linear Algebra and its Applications, 439 (2013): 1862 – 1874. [PDF preprint]

18. Computing Positive Semidefinite Minimum Rank for Small Graphs.. (2011 EGR)

Osborne and Warnberg. To appear in Involve.

19. Propagation time for zero forcing on a graph. (2011 REU)

Hogben, Huynh, Meyer, Kingsley, Walker, Young. Discrete Applied Mathematics, 160 (2012) 1994-2005.. [PDF preprint]
*
*

Catral, Cepek, Hogben, Huynh, Lazebnik, Peters, Young. Electronic Journal of Linear Algebra, 23 (2012), 906-922 [PDF]

21. Minimum rank, maximum nullity, and zero forcing number for simple digraphs. (2011)

A. Berliner, M. Catral, L. Hogben, M. Huynh, K. Lied, M. Young. . [PDF]

22. Minimum rank with zero diagonal. (2012 REUF)

C. Grood, J. Harmse, L. Hogben, T. Hunter, B. Jacob, A. Klimas, S. McCathern. To appear in Electronic Journal of Linear Algebra. [PDF]

24. Path cover number, maximum nullity, and zero forcing number of oriented graphs and other simple digraphs. (2013 REU) Adam Berliner, Cora Brown, Joshua Carlson, Nathanael Cox, Leslie Hogben, Jason Hu, Katrina Jacobs, Kathryn Manternach, Travis Peters, Nathan Warnberg, Michael Young. To appear in Involve. [PDF]

25. Minimum rank of graphs with loops. (2014 EGR)

Chassidy Bozeman, AnnaVictoria Ellsworth, Leslie Hogben, Jephian Chin-Hung Lin, Gabi Maurer, Kathleen Nowak, Aaron Rodriguez, James Strickland. [PDF]

REU 2013

REUF2012 meeting at ISU during summer 2013

summer 2010

Leslie Hogben's Homepage | June 2014 |