Igor Klep - Articles
To be published

(76) A Matrix Positivstellensatz with lifting polynomials , SIAM Journal on Optimization (with Jiawang Nie )

Published
2019

(75) Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions , Mem. Amer. Math. Soc. 257 vol. 1232 (2019), 104pp (with J. William Helton , Scott McCullough and
Markus Schweighofer )

(74) There are many more positive maps than completely positive maps , Int. Math. Res. Not. IMRN Issue 11 (2019) 3313--3375 (with Scott McCullough , Klemen Sivic and Aljaz Zalar ). Supplementary material (a Mathematica notebook file) is available as a nb file, and as a pdf file.

(73) Free bianalytic maps between spectrahedra and spectraballs in a generic setting , “Interpolation and Realization Theory with Applications to Control Theory” (Operator Theory: Advances and Applications vol. 272 ), edited by V. Bolotnikov, S. ter Horst, A.C.M. Ran, V. Vinnikov, 43–60, Birkhäuser, 2019 (with Meric Augat , J. William Helton and Scott McCullough )

2018

(72) Bianalytic Maps Between Free Spectrahedra , Math. Ann. 371 (2018) 883--959 (with Meric Augat , J. William Helton and Scott McCullough )

(71) Geometry of free loci and factorization of noncommutative polynomials , Adv. Math. 331 (2018) 589--626 (with J. William Helton and Jurij Volcic ). A preliminary version was published as Oberwolfach Preprint 2017-23

(70) Skolem-Noether algebras , J. Algebra 498 (2018) 294--314 (with Matej Brešar , Christoph Hanselka , Jurij Volcic )

(69) Positive trace polynomials and the universal Procesi-Schacher conjecture , Proc. Lond. Math. Soc. 117 (2018) 1101--1134 (with Špela Špenko and Jurij Volcic )

(68) Extreme points of matrix convex sets, free spectrahedra and dilation theory , J. Geom. Anal. 28 (2018) 1373–-1408 (with Eric Evert, J. William Helton and Scott McCullough ). The post-production version fixes issues identified by Tom Kriel and Ben Passer.

(67) Minimizer extraction in polynomial optimization is robust , SIAM J. Optim. 28 (2018) 3177--3207 (with Janez Povh , Jurij Volcic )

(66) The real spectrum of a noncommutative ring and the Artin-Lang homomorphism theorem , Algebr. Represent. Theory 21 (2018) 1--17

2017

(65) The tracial Hahn-Banach theorem, polar duals, matrix convex sets, and projections of free spectrahedra , J. Eur. Math. Soc. 19 (2017) 1845–1897 (with Bill Helton and Scott McCullough )

(64) Free loci of matrix pencils and domains of noncommutative rational functions , Comment. Math. Helvet. 92 (2017) 105--130 (with Jurij Volcic ). The post-production version contains an appendix due independently to Claudio Procesi and Špela Špenko .

(63) Free function theory through matrix invariants , Canad. J. Math. 69 (2017) 408--433 (with Špela Špenko )

(62) Regular and positive noncommutative rational functions , J. Lond. Math. Soc. 95 (2017) 613--632 (with James E. Pascoe and Jurij Volcic )

(61) Null- and Positivstellensätze for rationally resolvable ideals , Linear Algebra Appl. 527 (2017) 260--293 (with Victor Vinnikov and
Jurij Volčič )

(60) Circular Free Spectrahedra , J. Math. Anal. Appl. 445 (2017) 1047--1070 (with Eric Evert, J. William Helton and Scott McCullough )

2016

(59) Optimization of polynomials in non-commuting variables , SpringerBriefs in Mathematics , Springer-Verlag, XV, 104. ISBN 978-3-319-33336-6 (with Sabine Burgdorf
and
Janez Povh )

(58) Matrix Convex Hulls of Free Semialgebraic Sets , Trans. Amer. Math. Soc. 368 (2016) 3105--3139 (with J. William Helton and Scott McCullough ). Supplementary material (a Mathematica notebook file) is available here .

(57) Instances of the Kaplansky-Lvov multilinear conjecture for polynomials of degree three , Linear Algebra Appl. 508 (2016) 272--288 (with Ken Dykema ). Supplementary material (a Mathematica notebook file) is available as a nb file, and as a pdf file.

(56) Sweeping words and the length of a generic vector subspace of \(M_n(\mathbb F)\) , J. Combin. Theory Ser. A 143 (2016) 56--65 (with Špela Špenko )

(55) Constrained trace-optimization of polynomials in freely noncommuting variables , J. Global Optim. 64 (2016) 325--348 (with Janez Povh )

(54) On trace-convex noncommutative polynomials , Michigan Math. J. 65 (2016) 131--146
(with Scott McCullough and
Chris Nelson)

2015

(53) Rational sums of hermitian squares of free noncommutative polynomials , Ars Math. Contemp. 9 (2015) 253–269
(with Kristijan Cafuta and
Janez Povh ).

2014

(52) A tracial Nullstellensatz , Bull. Lond. Math. Soc. 46 (2014) 1091--1098 (with Špela Špenko )

(51) Noncommutative polynomials nonnegative on a variety intersect a convex set , J. Funct. Anal. 266 (2014) 6684--6752 (with J. William Helton and Chris Nelson)

(50) Addendum to “Connes’ embedding conjecture and sums of hermitian squares” , Adv. Math. 252 (2014) 805--811 (with Sabine Burgdorf ,
Ken Dykema and
Markus Schweighofer )

(49) On real one-sided ideals in a free algebra , J. Pure Appl. Algebra 218 (2014) 269--284 (with Jakob Cimprič , J. William Helton ,
Scott McCullough and Chris Nelson)

2013

(48) The matricial relaxation of a linear matrix inequality , Math. Program. 138 (2013) 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 .

(47) An exact duality theory for semidefinite programming based on sums of squares , Math. Oper. Res. 38 (2013) 569--590 (with Markus Schweighofer )

(46) A local-global principle for linear dependence of noncommutative polynomials , Israel J. Math. 193 (2013) 71--82 (with Matej Brešar )

(45) The tracial moment problem and trace-optimization of polynomials , Math. Program. 137 (2013) 557--578 (with Sabine Burgdorf , Kristijan Cafuta and
Janez Povh )

(44) Algorithmic aspects of sums of hermitian squares of noncommutative polynomials , Comput. Optim. Appl. 55 (2013) 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, 341–405, SIAM, 2013 (with J. William Helton and
Scott McCullough )

2012

(42) The convex Positivstellensatz in a free algebra , Adv. Math. 231 (2012) 516--534 (with J. William Helton and
Scott McCullough )

(41) The truncated tracial moment problem , J. Operator Theory 68 (2012) 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, 195–219, Birkhäuser, 2012
(with J. William Helton and
Scott McCullough )

(39) Constrained polynomial optimization problems with noncommuting variables , SIAM J. Optim. 22 (2012) 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, 377–405, Springer, 2012 (with J. William Helton and
Scott McCullough )

2011

(37) Trace-positive polynomials , Pacific J. Math. 250 (2011) 339--352

(36) Proper Analytic Free Maps , J. Funct. Anal. 260 (2011) 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) 28 (2011) (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, 79–101, Birkhäuser, 2011 (with Matej Brešar )

(33) Finite rings in which commutativity is transitive, Monatsh. Math. 162 (2011) 143--155 (with David Dolžan and
Primož Moravec )

(32) Analytic mappings between noncommutative pencil balls , J. Math. Anal. Appl. 376 (2011) 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. 26 (2011) 363--380 (with Kristijan Cafuta and
Janez Povh ). The accompanying MATLAB toolbox is NCSOStools .

2010

(30) The Procesi-Schacher conjecture and Hilbert's 17th problem for algebras with involution , J. Algebra 324 (2010) 256--268 (with Thomas Unger )

(29) Pure states, positive matrix polynomials and sums of hermitian squares , Indiana Univ. Math. J. 59 (2010) 857–874 (with Markus Schweighofer )

(28) A Note on Values of Noncommutative Polynomials , Proc. Amer. Math. Soc. 138 (2010) 2375--2379 (with Matej Brešar )

(27) A note on the nonexistence of sum of squares certificates for the BMV conjecture , J. Math. Phys. 51 (2010) 083521 (with Kristijan Cafuta and
Janez Povh )

(26) Semidefinite programming and sums of hermitian squares of noncommutative polynomials , J. Pure Appl. Algebra 214 (2010) 740--749 (with Janez Povh )

(25) Sign patterns for chemical reaction networks , J. Math. Chem. 47 (2010) 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. 17 (2010) 629--636 (with Primož Moravec )

(23) \(*\)-orderable semigroups, Semigroup Forum 80 (2010) 143--154 (with Primož Moravec )

(22) Trace-positive polynomials and the quartic tracial moment problem , C. R. Math. Acad. Sci. Paris 348 (2010) 721--726 (with Sabine Burgdorf )

(21) Relaxing LMI Domination Matricially , 49th IEEE Conference on Decision and Control (CDC) , 2010, 3331–3336 (with J. William Helton and
Scott McCullough )

2009

(20) Noncommutative ball maps , J. Funct. Anal. 257 (2009) 47--87 (with J. William Helton ,
Scott McCullough and
Nick Slinglend)

(19) Noncommutative Polynomials, Lie Skew-Ideals and Tracial Nullstellensätze , Math. Res. Lett. 16 (2009) 605--626 (with Matej Brešar )

(18) Determinant Expansions of Signed Matrices and of Certain Jacobians , SIAM J. Matrix Anal. Appl. 31 (2009) 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 6 (2009) 1388–1390 (with Thomas Unger )

2008

(16) Connes’ embedding conjecture and sums of hermitian squares , Adv. Math. 217 (2008) 1816--1837 (with Markus Schweighofer )

(15) Sums of hermitian squares and the BMV conjecture , J. Stat. Phys. 133 (2008) 739--760 (with Markus Schweighofer ).
Complimentary Mathematica notebook and its pdf output .

(14) The Joly-Becker theorem for \(*\)-orderings , Ann. Fac. Sci. Toulouse Math. 17 (2008) 81--92 (with Dejan Velušček< )

2007

(13) Embedding ordered valued domains into division rings , Algebr. Represent. Theory 10 (2007) 429--439

(12) A Nichtnegativstellensatz for polynomials in noncommuting variables , Israel J. Math. 161 (2007) 17--27 (with Markus Schweighofer )

(11) On valuations, places and graded rings associated to \(*\)-orderings , Can. Math. Bull. 50 (2007) 105--112

(10) The Prime Spectrum and the Extended Prime Spectrum of Noncommutative Rings , Algebr. Represent. Theory 10 (2007) 257--270 (with Marcus Tressl )

(09) Sums of hermitian squares, Connes’ embedding problem and the BMV Conjecture , Oberwolfach Reports 4 (2007) 779–782 (with Markus Schweighofer )

2006

(08) Embedding \(*\)-ordered domains into skew fields , J. Algebra 303 (2006) 416--429

(07) Generalized orderings and rings of fractions , Algebra Universalis 55 (2006) 93--109 (with Jakob Cimprič )

(06) Central extensions of \(*\)-ordered skew fields , Manuscripta Math. 120 (2006) 391--402 (with Dejan Velušček< )

2005

(05) On \(*\)-orderable groups , J. Pure Appl. Algebra 200 (2005) 25--35 (with Primož Moravec )

(04) Central extensions of n-ordered division rings , Comm. Algebra 33 (2005) 3265--3281 (with Dejan Velušček< )

2004

(03) A Kadison-Dubois representation for associative rings , J. Pure Appl. Algebra 189 (2004) 211--220

(02) The noncommutative graded Positivstellensatz , Comm. Algebra 32 (2004) 2029--2039

(01) n-real valuations and the higher level version of the Krull-Baer theorem , J. Algebra 279 (2004) 345--361 (with Dejan Velušček< )