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Monoid algebras and graph products
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2025
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Wilfried Imrich
Igor Klep
Daniel Smertnig
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A model theoretic perspective on matrix rings
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2025
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Igor Klep
Marcus Tressl
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Complete Upper Bound Hierarchies for Spectral Minimum in Noncommutative Polynomial Optimization
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2025
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Igor Klep
Victor Magron
Jurij Volčič
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PDF
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Duality, extreme points and hulls for noncommutative partial convexity
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2024
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Igor Klep
Scott McCullough
Tea Štrekelj
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PDF
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Upper bound hierarchies for noncommutative polynomial optimization
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2024
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Igor Klep
Victor Magron
Gaël Massé
Jurij Volčič
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A Random Copositive Matrix Is Completely Positive with Positive Probability
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2024
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Igor Klep
Tea Štrekelj
Aljaž Zalar
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PDF
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Matrix extreme points and free extreme points of free spectrahedra
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2024
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Aidan Epperly
Eric Evert
J. William Helton
Igor Klep
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PDF
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Monoid algebras and graph products
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2024
|
Wilfried Imrich
Igor Klep
Daniel Smertnig
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PDF
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Relaxations and Exact Solutions to Quantum Max Cut via the Algebraic Structure of Swap Operators
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2024
|
Adam Bene Watts
Anirban Chowdhury
Aidan Epperly
J. William Helton
Igor Klep
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Cross-positive linear maps, positive polynomials and sums of squares
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2024
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Igor Klep
Klemen Šivic
Aljaž Zalar
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Positivstellensätze and Moment problems with Universal Quantifiers
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2024
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Xiaomeng Hu
Igor Klep
Jiawang Nie
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State polynomials: positivity, optimization and nonlinear Bell inequalities
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2023
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Igor Klep
Victor Magron
Jurij Volčič
Jie Wang
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PDF
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Noncommutative Nullstellensätze and Perfect Games
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2023
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Adam Bene Watts
J. William Helton
Igor Klep
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PDF
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Ranks of linear matrix pencils separate simultaneous similarity orbits
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2023
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Harm Derksen
Igor Klep
Visu Makam
Jurij Volčič
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A random copositive matrix is completely positive with positive probability
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2023
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Igor Klep
Tea Štrekelj
Aljaž Zalar
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Sums of squares certificates for polynomial moment inequalities
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2023
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Igor Klep
Victor Magron
Jurij Volčič
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Relaxations and Exact Solutions to Quantum Max Cut via the Algebraic Structure of Swap Operators
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2023
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Adam Bene Watts
Anirban Chowdhury
Aidan Epperly
J. William Helton
Igor Klep
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Karush-Kuhn-Tucker conditions for non-commutative optimization problems
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2023
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Mateus Araújo
Igor Klep
Tamás Vértesi
Andrew J. P. Garner
Miguel Navascués
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Noncommutative Polynomial Optimization
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2022
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Abhishek Bhardwaj
Igor Klep
Victor Magron
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Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem
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2022
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Igor Klep
Claus Scheiderer
Jurij Volčič
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PDF
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Dimension-Free Entanglement Detection in Multipartite Werner States
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2022
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Felix Huber
Igor Klep
Victor Magron
Jurij Volčič
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PDF
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Facial structure of matrix convex sets
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2022
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Igor Klep
Tea Štrekelj
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Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem
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2022
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Igor Klep
Claus Scheiderer
Jurij Volčič
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Matrix Extreme Points and Free extreme points of Free spectrahedra
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2022
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Aidan Epperly
Eric Evert
J. William Helton
Igor Klep
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PDF
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Noncommutative Nullstellens\"atze and Perfect Games
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2021
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Adam Bene Watts
J. William Helton
Igor Klep
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PDF
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Noncommutative partially convex rational functions
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2021
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Michael T. Jury
Igor Klep
Mark E. Mancuso
Scott McCullough
J. E. Pascoe
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PDF
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Facial structure of matrix convex sets
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2021
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Igor Klep
Tea Štrekelj
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PDF
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Optimization Over Trace Polynomials
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2021
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Igor Klep
Victor Magron
Jurij Volčič
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PDF
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Positive univariate trace polynomials
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2021
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Igor Klep
J. E. Pascoe
Jurij Volčič
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PDF
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Sparse noncommutative polynomial optimization
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2021
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Igor Klep
Victor Magron
Janez Povh
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A Note on Group Representations, Determinantal Hypersurfaces and Their Quantizations
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2021
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Igor Klep
Jurij Volčič
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+
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Noncommutative Nullstellensätze and Perfect Games
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2021
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Adam Bene Watts
J. William Helton
Igor Klep
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+
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Ranks of linear matrix pencils separate simultaneous similarity orbits
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2021
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Harm Derksen
Igor Klep
Visu Makam
Jurij Volčič
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+
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Noncommutative Polynomial Optimization
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2021
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Abhishek Bhardwaj
Igor Klep
Victor Magron
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PDF
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Plurisubharmonic noncommutative rational functions
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2020
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Harry Dym
J. William Helton
Igor Klep
Scott McCullough
Jurij Volčič
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Noncommutative rational functions invariant under the action of a finite solvable group
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2020
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Igor Klep
J. E. Pascoe
Gregor Podlogar
Jurij Volčič
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PDF
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Optimization over trace polynomials
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2020
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Igor Klep
Victor Magron
Jurij Volčič
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PDF
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Noncommutative Polynomials Describing Convex Sets
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2020
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J. William Helton
Igor Klep
Scott McCullough
Jurij Volčič
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PDF
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Factorization of Noncommutative Polynomials and Nullstellensätze for the Free Algebra
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2020
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J. William Helton
Igor Klep
Jurij Volčič
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Noncommutative partially convex rational functions
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2020
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Michael T. Jury
Igor Klep
Mark E. Mancuso
Scott McCullough
J. E. Pascoe
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PDF
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Noncommutative Partial Convexity Via $$\Gamma $$-Convexity
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2020
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Michael T. Jury
Igor Klep
Mark E. Mancuso
Scott McCullough
J. E. Pascoe
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Local theory of free noncommutative functions: germs, meromorphic functions, and Hermite interpolation
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2020
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Igor Klep
Victor Vinnikov
Jurij Volčič
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Bianalytic free maps between spectrahedra and spectraballs
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2020
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J. William Helton
Igor Klep
Scott McCullough
Jurij Volčič
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Classifying minimal vanishing sums of roots of unity
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2020
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L Kovar Christie
Kenneth J. Dykema
Igor Klep
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PDF
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A Matrix Positivstellensatz with Lifting Polynomials
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2020
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Igor Klep
Jiawang Nie
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PDF
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Multipartite Rational Functions
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2020
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Igor Klep
Victor Vinnikov
Jurij Volčič
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Sparse Noncommutative Polynomial Optimization
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2019
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Igor Klep
Victor Magron
Janez Povh
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Factorization of noncommutative polynomials and Nullstellens\"atze for the free algebra
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2019
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J. William Helton
Igor Klep
Jurij Volčič
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PDF
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Free Bianalytic Maps between Spectrahedra and Spectraballs in a Generic Setting
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2019
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Meric Augat
J. William Helton
Igor Klep
Scott McCullough
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PDF
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Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions
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2019
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J. William Helton
Igor Klep
Scott McCullough
Markus Schweighofer
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Sparse Noncommutative Polynomial Optimization
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2019
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Igor Klep
Victor Magron
Janez Povh
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PDF
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Positive trace polynomials and the universal Procesi-Schacher conjecture
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2018
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Igor Klep
Špela Špenko
Jurij Volčič
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Geometry of free loci and factorization of noncommutative polynomials
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2018
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J. William Helton
Igor Klep
Jurij Volčič
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PDF
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Bianalytic maps between free spectrahedra
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2018
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Meric Augat
J. William Helton
Igor Klep
Scott McCullough
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A Model Theoretic Perspective on Matrix Rings
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2018
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Igor Klep
Marcus Tressl
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PDF
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Minimizer Extraction in Polynomial Optimization Is Robust
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2018
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Igor Klep
Janez Povh
Jurij Volčič
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Skolem–Noether algebras
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2017
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Matej Brešar
Christoph Hanselka
Igor Klep
Jurij Volčič
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PDF
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The Real Spectrum of a Noncommutative Ring and the Artin-Lang Homomorphism Theorem
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2017
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Igor Klep
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PDF
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There Are Many More Positive Maps Than Completely Positive Maps
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2017
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Igor Klep
Scott McCullough
Klemen Šivic
Aljaž Zalar
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PDF
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Extreme Points of Matrix Convex Sets, Free Spectrahedra, and Dilation Theory
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2017
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Eric Evert
J. William Helton
Igor Klep
Scott McCullough
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Null- and Positivstellensätze for rationally resolvable ideals
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2017
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Igor Klep
Victor Vinnikov
Jurij Volčič
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PDF
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The tracial Hahn–Banach theorem, polar duals, matrix convex sets, and projections of free spectrahedra
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2017
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J. William Helton
Igor Klep
Scott McCullough
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PDF
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Free loci of matrix pencils and domains of noncommutative rational functions
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2017
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Igor Klep
Jurij Volčič
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PDF
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Regular and positive noncommutative rational functions
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2017
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Igor Klep
J. E. Pascoe
Jurij Volčič
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Free bianalytic maps between spectrahedra and spectraballs in a generic setting
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2017
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Meric Augat
J. William Helton
Igor Klep
Scott McCullough
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Circular free spectrahedra
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2016
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Eric Evert
J. William Helton
Igor Klep
Scott McCullough
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Instances of the Kaplansky–Lvov multilinear conjecture for polynomials of degree three
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2016
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Kenneth J. Dykema
Igor Klep
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Sweeping words and the length of a generic vector subspace of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="double-struck">F</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>
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2016
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Igor Klep
Špela Špenko
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PDF
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On trace-convex noncommutative polynomials
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2016
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Igor Klep
Scott McCullough
Christopher Nelson
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Optimization of Polynomials in Non-Commuting Variables
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2016
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Sabine Burgdorf
Igor Klep
Janez Povh
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Eigenvalue Optimization of Polynomials in Non-commuting Variables
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2016
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Sabine Burgdorf
Igor Klep
Janez Povh
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Cyclic Equivalence to Sums of Hermitian Squares
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2016
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Sabine Burgdorf
Igor Klep
Janez Povh
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+
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Detecting Sums of Hermitian Squares
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2016
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Sabine Burgdorf
Igor Klep
Janez Povh
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Selected Results from Algebra and Mathematical Optimization
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2016
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Sabine Burgdorf
Igor Klep
Janez Povh
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The tracial Hahn-Banach theorem and matrix convex sets
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2016
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Igor Klep
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Trace Optimization of Polynomials in Non-commuting Variables
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2016
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Sabine Burgdorf
Igor Klep
Janez Povh
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PDF
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Free Function Theory Through Matrix Invariants
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2015
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Igor Klep
Špela Špenko
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PDF
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Matrix convex hulls of free semialgebraic sets
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2015
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J. William Helton
Igor Klep
Scott McCullough
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Constrained trace-optimization of polynomials in freely noncommuting variables
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2015
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Igor Klep
Janez Povh
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PDF
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Rational sums of hermitian squares of free noncommutative polynomials
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2015
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Kristijan Cafuta
Igor Klep
Janez Povh
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+
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Multipartite rational functions
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2015
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Igor Klep
Victor Vinnikov
Jurij Volčič
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+
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Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions
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2014
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J. William Helton
Igor Klep
Scott McCullough
Markus Schweighofer
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Inclusion of spectrahedra, dilations, the matrix cube problem and coin tossing
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2014
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J. William Helton
Igor Klep
Scott McCullough
Markus Schweighofer
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PDF
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A tracial Nullstellensatz
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2014
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Igor Klep
Špela Špenko
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Noncommutative polynomials nonnegative on a variety intersect a convex set
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2014
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J. William Helton
Igor Klep
Christopher Nelson
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+
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Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions
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2014
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J. William Helton
Igor Klep
Scott McCullough
Markus Schweighofer
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PDF
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Addendum to “Connesʼ embedding conjecture and sums of hermitian squares” [Adv. Math. 217 (4) (2008) 1816–1837]
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2013
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Sabine Burgdorf
Ken Dykema
Igor Klep
Markus Schweighofer
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PDF
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On real one-sided ideals in a free algebra
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2013
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Jakob Cimprič
J. William Helton
Igor Klep
Scott McCullough
Christopher Nelson
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PDF
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An Exact Duality Theory for Semidefinite Programming Based on Sums of Squares
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2013
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Igor Klep
Markus Schweighofer
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Free Convex Algebraic Geometry
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2013
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J. William Helton
Igor Klep
Scott McCullough
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Chapter 8: Free Convex Algebraic Geometry
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2012
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J. William Helton
Igor Klep
Scott McCullough
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ON THE COMPLEXITY OF SEMIDEFINITE PROGRAMS ARISING IN POLYNOMIAL OPTIMIZATION
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2012
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Igor Klep
Janez Povh
Angelika Wiegele
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Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials
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2012
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Sabine Burgdorf
Kristijan Cafuta
Igor Klep
Janez Povh
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+
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The convex Positivstellensatz in a free algebra
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2012
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J. William Helton
Igor Klep
Scott McCullough
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PDF
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A local-global principle for linear dependence of noncommutative polynomials
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2012
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Matej Brešar
Igor Klep
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PDF
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The matricial relaxation of a linear matrix inequality
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2012
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J. William Helton
Igor Klep
Scott McCullough
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PDF
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The truncated tracial moment problem
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2012
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Sabine Burgdorf
Igor Klep
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+
PDF
Chat
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Free Analysis, Convexity and LMI Domains
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2012
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J. William Helton
Igor Klep
Scott McCullough
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+
PDF
Chat
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Constrained Polynomial Optimization Problems with Noncommuting Variables
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2012
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Kristijan Cafuta
Igor Klep
Janez Povh
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PDF
Chat
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The truncated tracial moment problem
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2012
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Sabine Burgdorf
Igor Klep
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+
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Free analysis, convexity and LMI domains
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2012
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J. William Helton
Igor Klep
Scott McCullough
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+
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Algorithmic aspects of sums of hermitian squares
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2012
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Sabine Burgdorf
Kristijan Cafuta
Igor Klep
Janez Povh
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+
PDF
Chat
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Semidefinite programming in matrix unknowns which are dimension free
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2011
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J. William Helton
Igor Klep
Scott McCullough
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PDF
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The tracial moment problem and trace-optimization of polynomials
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2011
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Sabine Burgdorf
Kristijan Cafuta
Igor Klep
Janez Povh
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PDF
Chat
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Convexity and Semidefinite Programming in Dimension-Free Matrix Unknowns
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2011
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J. William Helton
Igor Klep
Scott McCullough
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NCSOStools: a computer algebra system for symbolic and numerical computation with noncommutative polynomials
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2011
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Kristijan Cafuta
Igor Klep
Janez Povh
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+
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Infeasibility certificates for linear matrix inequalities
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2011
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Igor Klep
Markus Schweighofer
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+
PDF
Chat
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Trace-positive polynomials
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2011
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Igor Klep
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Tracial Nullstellensätze
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2011
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Matej Brešar
Igor Klep
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+
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Infeasibility certificates for linear matrix inequalities
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2011
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Igor Klep
Markus Schweighofer
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Lie Algebras with Abelian Centralizers
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2010
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Igor Klep
Primož Moravec
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Relaxing LMI domination matricially
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2010
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J. William Helton
Igor Klep
Scott McCullough
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OPTIMIZATION AND APPROXIMATION OF NC POLYNOMIALS WITH SUMS OF SQUARES
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2010
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Kristijan Cafuta
Igor Klep
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+
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Analytic mappings between noncommutative pencil balls
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2010
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J. William Helton
Igor Klep
Scott McCullough
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+
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Proper analytic free maps
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2010
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J. William Helton
Igor Klep
Scott McCullough
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A note on the nonexistence of sum of squares certificates for the Bessis–Moussa–Villani conjecture
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2010
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Kristijan Cafuta
Igor Klep
Janez Povh
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PDF
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Trace-positive polynomials and the quartic tracial moment problem
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2010
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Sabine Burgdorf
Igor Klep
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PDF
Chat
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The Procesi–Schacher conjecture and Hilbert's 17th problem for algebras with involution
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2010
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Igor Klep
Thomas Unger
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A note on values of noncommutative polynomials
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2010
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Matej Brešar
Igor Klep
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PDF
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Pure states, positive matrix polynomials and sums of hermitian squares
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2010
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Igor Klep
Markus Schweighofer
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Relaxing linear matrix inequalities noncommutatively
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2010
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Igor Klep
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Scheiderer, Claus (D-KNST-MS): Positivity and sums of squares: a guide to recent results. (English summary). - Emerging applications of algebraic geometry, 271-324, IMA Vol. Math. Appl., 149, Springer, New York, 2009
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2010
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Igor Klep
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The tracial moment problem and trace-positive polynomials
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2010
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Igor Klep
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The truncated tracial moment problem
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2010
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Sabine Burgdorf
Igor Klep
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*-orderable semigroups
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2009
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Igor Klep
Primož Moravec
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PDF
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Sign patterns for chemical reaction networks
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2009
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J. William Helton
Vitaly Katsnelson
Igor Klep
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Semidefinite programming and sums of hermitian squares of noncommutative polynomials
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2009
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Igor Klep
Janez Povh
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+
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Finite rings in which commutativity is transitive
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2009
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David Dolžan
Igor Klep
Primož Moravec
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Noncommutative ball maps
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2009
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J. William Helton
Igor Klep
Scott McCullough
Nick Slinglend
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PDF
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Determinant Expansions of Signed Matrices and of Certain Jacobians
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2009
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J. William Helton
Igor Klep
Raul Gomez
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Values of Noncommutative Polynomials, Lie Skew-Ideals and Tracial Nullstellensätze
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2009
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Matej Brešar
Igor Klep
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The Joly–Becker theorem for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>*</mml:mo></mml:math>–orderings
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2008
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Igor Klep
Dejan Velušček
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PDF
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Sums of Hermitian Squares and the BMV Conjecture
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2008
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Igor Klep
Markus Schweighofer
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PDF
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Connes' embedding conjecture and sums of hermitian squares
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2007
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Igor Klep
Markus Schweighofer
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PDF
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A Nichtnegativstellensatz for polynomials in noncommuting variables
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2007
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Igor Klep
Markus Schweighofer
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Embedding Ordered Valued Domains into Division Rings
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2007
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Igor Klep
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On Valuations, Places and Graded Rings Associated to ∗-Orderings
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2007
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Igor Klep
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The Prime Spectrum and the Extended Prime Spectrum of Noncommutative Rings
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2006
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Igor Klep
Marcus Tressl
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Central Extensions of *-ordered Skew Fields
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2006
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Igor Klep
Dejan Velušček
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Embedding ∗-ordered domains into skew fields
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2006
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Igor Klep
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Generalized orderings and rings of fractions
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2006
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Jaka Cimprič
Igor Klep
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Central Extensions of <i>n</i>-Ordered Division Rings
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2005
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Igor Klep
Dejan Velušček
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On <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mo>*</mml:mo></mml:math>-orderable groups
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2005
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Igor Klep
Primož Moravec
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The Noncommutative Graded Positivstellensatz
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2004
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Igor Klep
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n-real valuations and the higher level version of the Krull–Baer theorem
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2004
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Igor Klep
Dejan Velušček
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A Kadison–Dubois representation for associative rings
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2004
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Igor Klep
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ORDERINGS OF HIGHER LEVEL AND RINGS OF FRACTIONS
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2001
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Jaka Cimpri
Igor Klep
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