Murray Marshall's Home Page

Position

Professor, Department of Mathematics and Statistics, University of Saskatchewan

University Address

106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada
Phone Number: (306) 966-6098
E-mail address: marshall@math.usask.ca

Personal Information

My parents were raised in the area around Moose Jaw, Saskatchewan. They settled (as farmers, although my mother had earlier been a teacher) in the Etomami district in northeastern Saskatchewan, in 1931. I was born there, at the outpost hospital in the nearby town of Hudson Bay, on March 24, 1940. I have 3 children, Ian, Aaron and Christopher, and 6 grandchildren.

Research Interests

My research interests include: Quadratic Forms, Spaces of Orderings, Real Algebraic Geometry, Positive Polynomials and Sums of Squares

Some Links

Mathematics Genealogy Project, U of S Electronic Theses, Oberwolfach Photo Collection, ArXiv/Org , RAAG Preprint Server, Valuation Theory Home Page, Algebra and Logic Seminar, Seminaire Structures Algebriques Ordonnees, Konstanz Group, Ljubljana Group, SIAG-AG

NSERC Undergraduate Students

Erin Dramnitzki (Max-Cut Algorithm, 2005)

Graduate Students

Mehdi Ghasemi (PhD, 2009 - )
Wei Fan (MSc, 2004 - 2006)
Pawel Gladki (PhD, 2003 - 2007)

Predoctoral Fellows

Tim Netzer, May-Oct. 2007

Postdoctoral Fellows

Katarzyna Osiak, Aug.-Oct. 2008
Andreas Fischer, 2006 - 2008
Igor Klep, May-Sept. 2006

Published Works

1. Positive Polynomials and Sums of Squares

M. Ghasemi, M. Marshall, Lower bounds for a polynomial in terms of its coefficients, to appear. original: (pdf file) revised: (pdf file)
J. Cimpric, M. Marshall, T. Netzer, Closures of quadratic modules, Israel J. Math., to appear. original: (pdf file) revised: (pdf file)
J. Cimpric, M. Marshall, T. Netzer, On the real multidimensional rational K-moment problem, Transactions AMS, to appear. original: (pdf file) revised: (pdf file)
M. Marshall, Polynomials non-negative on a strip, Proceedings AMS, 138 (2010) 1559-1567. (pdf file)
J. Cimpric, S. Kuhlmann, M. Marshall, Positivity in power series rings, Advances in Geometry, to appear. original: (pdf file) revised: (pdf file)
M. Marshall, Cylinders with compact cross-section and the strip conjecture, Seminaire de Structures Algebriques Ordonnes Prepublications 81 (2009), Univ. Paris 7. (pdf file)
M. Marshall, Representation of non-negative polynomials, degree bounds and applications to optimization, Canad. J. Math., 61 (2009) 205-221. (pdf file)
M. Marshall, Positive polynomials and sums of squares, AMS Math. Surveys and Monographs 146 (2008) 187+xii pages. (book info)
M. Marshall, Representation of non-negative polynomials with finitely many zeros, Annales de la Faculte des Sciences Toulouse 15 (2006) 599-609.(pdf file)
M. Marshall, Error estimates in the optimization of degree two polynomials on a discrete hypercube, SIAM Journal on Optimization, 16 (2005) 297-309. original: (ps file) revised: (pdf file)
S. Kuhlmann, M. Marshall, N. Schwartz, Positivity, sums of squares and the multi-dimensional moment problem II, Advances in Geometry, 5 (2005) 583-606. (pdf file)

2. PP Conjecture

P. Gladki, M. Marshall, On families of testing formulae for a pp formula, Cont. Math. 493 (2009) 181-188. (pdf file)
P. Gladki, M. Marshall, The pp conjecture for the space of orderings of the field R(x,y), J. Pure & Applied Algebra, 212 (2008) 197-203. (pdf file)
P. Gladki, M. Marshall, The pp conjecture for spaces of orderings of rational conics, Algebra and its Applications, 6 (2007) 245-257. (pdf file)
M. Marshall, Local-global properties of positive primitive formulas in the theory of spaces of orderings, J. Symbolic Logic, 71 (2006) 1097-1107. (pdf file)
M. Dickmann, M. Marshall, F. Miraglia, Lattice ordered reduced special groups, Annals of Pure and Applied Logic, 132 (2005) 27-49.

3. Other Topics

S. Kuhlmann, M. Marshall, K. Osiak, Cyclic 2-structures and spaces of orderings of power series fields in two variables, to appear. (pdf file)
A. Fischer, M. Marshall, Extending piecewise polynomial functions in two variables, to appear. (pdf file)
M. Machura, M. Marshall, K. Osiak, Metrizability of the space of R-places of a real function field, Math. Zeit., to appear. original: (pdf file) revised: (pdf file)
D. Gondard, M. Marshall, Real holomorphy rings and the complete real spectrum, Annales de la Faculte des Sciences Toulouse, to appear. (pdf file)
J. Cimpric, M. Kochetov, M. Marshall, Orderability of pointed cocommutative Hopf algebras, Algebras and Representation Theory (2007) 25-54. (pdf file)
M. Marshall, Real reduced multirings, J. Pure & Applied Algebra, 205 (2006) 452-468. (pdf file)