Preprints | ||
| (51) | Correction of a proof in "Connes' embedding conjecture and sums of hermitian squares", latest revision 31 Mar 2013. (with Sabine Burgdorf, Ken Dykema, Markus Schweighofer). | |
| (50) | The real spectrum of a noncommutative ring and the Artin-Lang homomorphism theorem, latest revision 28 Jan 2010. | |
To Be Published | ||
| (50) | On real one-sided ideals in a free algebra, Journal of Pure and Applied Algebra. (with Jaka Cimprič, J. William Helton, Scott McCullough, and Chris Nelson). | |
| (49) | An exact duality theory for semidefinite programming based on sums of squares, Mathematics of Operations Research. (with Markus Schweighofer). | |
Published | ||
2013 | ||
| (47) | The matricial relaxation of a linear matrix inequality, Math. Program., 2013, vol. 138, pp. 401-445. (with J. William Helton and Scott McCullough). Supplementary material (a zip file containing three Mathematica notebooks and their pdf versions) is available here. | |
| (46) | A local-global principle for linear dependence of noncommutative polynomials, Israel J. Math., 2013, vol. 193, pp. 71-82. (with Matej Brešar). | |
| (45) | The tracial moment problem and trace-optimization of polynomials, Math. Program., 2013, vol. 137, pp. 557-578. (with Sabine Burgdorf, Kristijan Cafuta and Janez Povh). | |
| (44) | Algorithmic aspects of sums of hermitian squares of noncommutative polynomials, Comput. Optim. Appl., 2013, vol. 55, pp. 137-153.(with Sabine Burgdorf, Kristijan Cafuta and Janez Povh). | |
| (43) | Free convex algebraic geometry, "Semidefinite Optimization and Convex Algebraic Geometry" edited by G. Blekherman, P. Parrilo, R. Thomas, pp. 341-405, SIAM, 2013. (with J. William Helton and Scott McCullough). | |
2012 | ||
| (42) | The convex Positivstellensatz in a free algebra, Adv. Math., 2012, vol. 231, pp. 516-534. (with J. William Helton and Scott McCullough). | |
| (41) | The truncated tracial moment problem, J. Operator Theory, 2012, vol. 68, pp. 141-163. (with Sabine Burgdorf). | |
| (40) | 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, pp. 195-219, Birkhäuser, 2012. (with J. William Helton and Scott McCullough). | |
| (39) | Constrained polynomial optimization problems with noncommuting variables, SIAM J. Optim., 2012, vol. 22, pp. 363-383. (with Kristijan Cafuta and Janez Povh). | |
| (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: 27 Apr 13