Preprints
(47) The convex Positivstellensatz in a free algebra, latest revision 20 Oct 2011. (with J. William Helton and Scott McCullough).
(46) The matricial relaxation of a linear matrix inequality, latest revision 1 Jun 2011. (with J. William Helton and Scott McCullough). Supplementary material (a zip file containing three Mathematica notebooks and their pdf versions) is available here.
(45) The real spectrum of a noncommutative ring and the Artin-Lang homomorphism theorem, latest revision 28 Jan 2010.
 

To Be Published

(44) Free analysis, convexity and LMI domains, "Mathematical methods in systems, optimization and control" (Operator Theory: Advances and Applications) edited by H. Dym, M. de Oliveira, M. Putinar, Birkhäuser, 2012. (with J. William Helton and Scott McCullough).
(43) Constrained polynomial optimization problems with noncommuting variables, SIAM Journal on Optimization. (with Kristijan Cafuta and Janez Povh).
(42) Free convex algebraic geometry, "Semidefinite Optimization and Convex Algebraic Geometry" edited by G. Blekherman, P. Parrilo, R. Thomas, SIAM, 2012. (with J. William Helton and Scott McCullough).
(41) The tracial moment problem and trace-optimization of polynomials, Mathematical Programming. (with Sabine Burgdorf, Kristijan Cafuta and Janez Povh).
(40) A local-global principle for linear dependence of noncommutative polynomials, Israel Journal of Mathematics. (with Matej Brešar).
(39) The truncated tracial moment problem, Journal of Operator Theory. (with Sabine Burgdorf).
 

Published

2012

(38) Convexity and Semidefinite Programming in dimension-free matrix unknowns, "Handbook of Semidefinite, Conic and Polynomial Optimization" edited by M. Anjos and J. B. Lasserre, pp. 377-405, Springer, 2012. (with J. William Helton and Scott McCullough).
 

2011

(37) Trace-positive polynomials, Pacific J. Math., 2011, vol. 250, pp. 339-352.
(36) Proper Analytic Free Maps, J. Funct. Anal., 2011, vol. 260, pp. 1476-1490. (with J. William Helton and Scott McCullough). Supplementary material (a zip file containing a Mathematica notebook and its pdf version) is available here.
(35) Infeasibility certificates for linear matrix inequalities, Oberwolfach Preprints (OWP), 2011, vol. 28. (with Markus Schweighofer).
(34) Tracial Nullstellensätze, "Notions of Positivity and the Geometry of Polynomials" (J. Borcea memorial volume) edited by P. Brändén, M. Passare and M. Putinar, pp. 79-101, Birkhäuser, 2011. (with Matej Brešar).
(33) Finite rings in which commutativity is transitive, Monatsh. Math., 2011, vol. 162, pp. 143-155. (with David Dolžan and Primož Moravec).
(32) Analytic mappings between noncommutative pencil balls, J. Math. Anal. Appl., 2011, vol. 376, pp. 407-428. (with J. William Helton and Scott McCullough).
(31) NCSOStools: a computer algebra system for symbolic and numerical computation with noncommutative polynomials, Optim. Methods Softw., 2011, vol. 26, pp. 363-380. (with Kristijan Cafuta and Janez Povh). The accompanying MATLAB toolbox: NCSOStools.
 

2010

(30) The Procesi-Schacher conjecture and Hilbert's 17th problem for algebras with involution, J. Algebra, 2010, vol. 324, no. 2, pp. 256-268. (with Thomas Unger).
(29) Pure states, positive matrix polynomials and sums of hermitian squares, Indiana Univ. Math. J., 2010, vol. 59, no. 3, pp. 857-874. (with Markus Schweighofer).
(28) A Note on Values of Noncommutative Polynomials, Proc. Amer. Math. Soc., 2010, vol. 138, no. 7, pp. 2375-2379. (with Matej Brešar).
(27) A note on the nonexistence of sum of squares certificates for the BMV conjecture, J. Math. Phys., 2010, vol. 51, no. 8, 083521. (with Kristijan Cafuta and Janez Povh).
(26) Semidefinite programming and sums of hermitian squares of noncommutative polynomials, J. Pure Appl. Algebra, 2010, vol. 214, pp. 740-749. (with Janez Povh).
(25) Sign patterns for chemical reaction networks, J. Math. Chem., 2010, vol. 47, no. 1, pp. 403-429. (with J. William Helton and Vitaly Katsnelson). Accompanying Chemical Reaction Network Software runs under Mathematica.
(24) Lie algebras with abelian centralizers, Algebra Colloq., 2010, vol. 17, no. 4, pp. 629-636. (with Primož Moravec).
(23) *-orderable semigroups, Semigroup Forum, 2010, vol. 80, pp. 143-154. (with Primož Moravec).
(22) Trace-positive polynomials and the quartic tracial moment problem, C. R. Math. Acad. Sci. Paris, 2010, vol. 348, no. 13-14, pp. 721-726. (with Sabine Burgdorf).
(21) Relaxing LMI Domination Matricially, in 49th IEEE Conference on Decision and Control (CDC), 2010, pp. 3331-3336. (with J. William Helton and Scott McCullough).
 

2009

(20) Noncommutative ball maps, J. Funct. Anal., 2009, vol. 257, pp. 47-87. (with J. William Helton, Scott McCullough and Nick Slinglend).
(19) Noncommutative Polynomials, Lie Skew-Ideals and Tracial Nullstellensätze, , Math. Res. Lett., 2009, vol. 16, pp. 605-626. (with Matej Brešar).
(18) Determinant Expansions of Signed Matrices and of Certain Jacobians, SIAM J. Matrix Anal. Appl., 2009, vol. 31, pp. 732-754. (with J. William Helton and Raul Gomez). Accompanying Chemical Reaction Network Software (under Mathematica) can be found here.
(17) The Procesi-Schacher conjecture and Hilbert's 17th problem for algebras with involution, Oberwolfach Reports, 2009, vol.6, no. 2, pp. 1388-1390. (with Thomas Unger).
 

2008

(16) Connes' embedding conjecture and sums of hermitian squares, , Adv. Math., 2008, vol. 217, pp. 1816-1837. (with Markus Schweighofer).
(15) Sums of hermitian squares and the BMV conjecture, J. Stat. Phys., 2008, vol. 133, pp. 739-760. Complimentary Mathematica notebook and its pdfversion. (with Markus Schweighofer).
(14) *-version of the Joly-Becker theorem, Ann. Fac. Sci. Toulouse Math., 2008, vol. 17, pp. 81-92. (with Dejan Velušček).
 

2007

(13) Embedding ordered valued domains into division rings, Algebr. Represent. Theory, 2007, vol. 10, pp. 429-439.
(12) A Nichtnegativstellensatz for polynomials in noncommuting variables, Israel J. Math.,2007, vol. 161, pp. 17-27. (with Markus Schweighofer).
(11) On valuations, places and graded rings associated to *-orderings, Can. Math. Bull., 2007, Vol. 50, pp. 105-112.
(10) The Prime Spectrum and the Extended Prime Spectrum of Noncommutative Rings, Algebr. Represent. Theory, 2007, Vol. 10, pp. 257-270. (with Marcus Tressl).
(09) Sums of hermitian squares, Connes' embedding problem and the BMV Conjecture, Oberwolfach Reports, 2007, vol.4, no. 1, pp. 779-782. (with Markus Schweighofer).
 

2006

(08) Embedding *-ordered domains into skew fields, J. Algebra, 2006, vol. 303, pp. 416-429.
(07) Generalized orderings and rings of fractions, Algebra Universalis, 2006, vol. 55, pp. 93-109. (with Jaka Cimprič).
(06) Central extensions of *-ordered skew fields, Manuscripta Math., 2006, vol. 120, pp. 391-402. (with Dejan Velušček).
 

2005

(05) On *-orderable groups, J. Pure Appl. Algebra, 2005, vol. 200, pp. 25-35. (with Primož Moravec).
(04) Central extensions of n-ordered division rings, Comm. Algebra, 2005, vol. 33, pp. 3265-3281. (with Dejan Velušček).
 

2004

(03) A Kadison-Dubois representation for associative rings, J. Pure Appl. Algebra, 2004, vol. 189, pp. 211-220.
(02) The noncommutative graded Positivstellensatz, Comm. Algebra, 2004, vol. 32, pp. 2029-2039.
(01) n-real valuations and the higher level version of the Krull-Baer theorem, J. Algebra, 2004, vol. 279, pp. 345-361. (with Dejan Velušček)



  Last changes: 2 Jan 12