Murray Marshall's Home Page

Position

Professor Emeritus, 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

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, Nonassociative Algebra Seminar, Seminaire Structures Algebriques Ordonnees, Katowice Seminar, Konstanz Group, BIRS, SIGSAM, SIAG-AG, Leipzig 2011, Magdeburg 2012

Graduate Students

Mehdi Ghasemi (PhD, 2009 - 2012)
Pawel Gladki (PhD, 2003 - 2007)
Wei Fan (MSc, 2004 - 2006)

Predoctoral Fellows

Tim Netzer, May-Oct. 2007

Postdoctoral Fellows

Sven Wagner, 2010 - 2011
Pawel Gladki, July-Sept. 2010
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, S. Kuhlmann, M. Marshall, Application of Jacobi's representation theorem to locally multiplicatively convex topological R-algebras, to appear: (pdf file)
M. Ghasemi, J.B. Lasserre, M. Marshall, Lower bounds on the global minimum of a polynomial, to appear: (pdf file)
M. Marshall, Application of localization to the multivariate moment problem, Math. Scand., to appear: (pdf file) revised: (pdf file)
M. Ghasemi, M. Marshall, Sven Wagner, Closure of the cone of sums of 2d-powers in certain weighted \ell_1-seminorm topologies, Canad. Math. Bull., to appear: (pdf file)
M. Ghasemi, M. Marshall, Lower bounds for polynomials using geometric programming, SIAM Journal on Optimization, 22 (2012) 460-473. original: (pdf file) revised: (pdf file)
M. Marshall, T. Netzer, Positivstellensatze for real function algebras, Math. Zeitschrift, 270 (2012) 889-901. (pdf file)
J. Cimpric, M. Marshall, T. Netzer, Closures of quadratic modules, Israel J. Math., 189 (2011) 445-474. original: (pdf file) revised: (pdf file)
J. Cimpric, M. Marshall, T. Netzer, On the real multidimensional rational K-moment problem, Transactions AMS, 363 (2011) 5773-5788. original: (pdf file) revised: (pdf file)
M. Ghasemi, M. Marshall, Lower bounds for a polynomial in terms of its coefficients, Archiv der Mathematik, 95 (2010) 343-353. 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, 10 (2010) 135-143. 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. Orderings, Valuations and Quadratic Forms

P. Gladki, M. Marshall, Quotients of index two and general quotients in a space of orderings, Oberwolfach Preprint 2011-36, to appear. (pdf file)
P. Gladki, M. Marshall, Orderings and signatures of higher level on multirings and hyperfields, J. K-Theory, 10 (2012) 489-518. original: (pdf file) revised: (pdf file)
S. Kuhlmann, M. Marshall, K. Osiak, Cyclic 2-structures and spaces of orderings of power series fields in two variables, J. Algebra, 335 (2011) 36-48. original: (pdf file) revised: (pdf file)
M. Machura, M. Marshall, K. Osiak, Metrizability of the space of R-places of a real function field, Math. Zeitschrift, 266 (2010) 237-242. 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 19 (2010), Fascicule Special, 57-74. (pdf file)
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)
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 and multifields, J. Pure & Applied Algebra, 205 (2006) 452-468. (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

A. Fischer, M. Marshall, Extending piecewise polynomial functions in two variables, Annales de la Faculte des Sciences Toulouse, to appear. original: (pdf file) revised: (pdf file)