Jurij Volčič

• Real algebraic geometry
• Free analysis
• Noncommutative algebra
• Invariant theory
• Quantum information
• Polynomial optimization

Experience

Research

Published papers

1. J. Volčič: Dimension-free matricial Nullstellensätze for noncommutative polynomials, in Recent Progress in Ring and Factorization Theory, 439-450, Springer Proc. Math. Stat. 477, Springer, Cham, 2025 (arXiv, pdf)
2. I. Klep, V. Magron, J. Volčič: Sums of squares certificates for polynomial moment inequalities, Found. Comput. Math. (2025) (arXiv, pdf)
3. F. Huber, V. Magron, J. Volčič: Positivity of state, trace, and moment polynomials, and applications in quantum information, in Operator Theory, 2nd ed., Springer, Basel, 2025 (arXiv, pdf)
4. J. Volčič: Linear matrix pencils and noncommutative convexity, in Operator Theory, 2nd ed., Springer, Basel, 2025 (arXiv, pdf)
5. R. Chen, L. Mančinska, J. Volčič: All real projective measurements can be self-tested, Nat. Phys. 20 (2024) 1642-1647 (arXiv, pdf)
6. J. Volčič: Constant-sized self-tests for maximally entangled states and single projective measurements, Quantum 8 (2024) 1292 (arXiv, pdf)
7. I. Klep, V. Magron, J. Volčič, J. Wang: State polynomials: positivity, optimization and nonlinear Bell inequalities, Math. Program. 207 (2024) 645-691 (arXiv, pdf)
8. H. Derksen, I. Klep, V. Makam, J. Volčič: Ranks of linear matrix pencils separate simultaneous similarity orbits, Adv. Math. 415 (2023) 108888 (arXiv, pdf)
9. I. Klep, C. Scheiderer, J. Volčič: Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem, Math. Ann. 387 (2022) 1403-1433 (arXiv, pdf)
10. J. W. Helton, I. Klep, J. Volčič: Factorization of noncommutative polynomials and Nullstellensätze for the free algebra, Int. Math. Res. Not. 1 (2022) 343-372 (arXiv, pdf)
11. F. Huber, I. Klep, V. Magron, J. Volčič: Dimension-free entanglement detection in multipartite Werner states, Commun. Math. Phys. 396 (2022) 1051-1070 (arXiv, pdf)
12. K. Aguilar, Á. Chávez, S. R. Garcia, J. Volčič: Norms on complex matrices induced by complete homogeneous symmetric polynomials, Bull. Lond. Math. Soc. 54 (2022) 2078-2100 (arXiv, pdf)
13. I. Klep, V. Magron, J. Volčič: Optimization over trace polynomials, Ann. Henri Poincaré 23 (2022) 67-100 (arXiv, pdf)
14. J. W. Helton, I. Klep, S. McCullough, J. Volčič: Noncommutative polynomials describing convex sets, Found. Comput. Math. 21 (2021) 575-611 (arXiv, pdf)
15. I. Klep, J. E. Pascoe, J. Volčič: Positive univariate trace polynomials, J. Algebra 579 (2021) 303-317 (arXiv, pdf)
16. J. Volčič: Hilbert's 17th problem in free skew fields, Forum Math. Sigma 9 (2021) E61 (arXiv, pdf)
17. H. Dym, J. W. Helton, I. Klep, S. McCullough, J. Volčič: Plurisubharmonic noncommutative rational functions, J. Math. Anal. Appl. 492 (2020) 124421, 23 pp (arXiv, pdf)
18. I. Klep, V. Vinnikov, J. Volčič: Multipartite rational functions, Doc. Math. 25 (2020) 1285-1313 (arXiv, pdf)
19. I. Klep, J. E. Pascoe, G. Podlogar, J. Volčič: Noncommutative rational functions invariant under the action of a finite solvable group, J. Math. Anal. Appl. 490 (2020) 124341, 17 pp (arXiv, pdf)
20. J. Volčič: Free Bertini's theorem and applications, Proc. Amer. Math. Soc. 148 (2020) 3661-3671 (arXiv, pdf)
21. I. Klep, V. Vinnikov, J. Volčič: Local theory of free noncommutative functions: germs, meromorphic functions and Hermite interpolation, Trans. Amer. Math. Soc. 373 (2020) 5587-5625 (arXiv, pdf)
22. I. Klep, J. Volčič: A note on group representations, determinantal hypersurfaces and their quantizations, in Operator Theory, Functional Analysis and Applications, 393-402, Oper. Theory Adv. Appl. 282, Birkhäuser/Springer, Cham, 2020 (pdf)
23. J. W. Helton, I. Klep, S. McCullough, J. Volčič: Bianalytic free maps between spectrahedra and spectraballs, J. Funct. Anal. 278 (2020) 108472, 61 pp (arXiv, pdf)
24. J. Volčič: Stable noncommutative polynomials and their determinantal representations, SIAM J. Appl. Algebra Geometry 3 (2019) 152-171 (arXiv, pdf)
25. J. W. Helton, I. Klep, J. Volčič: Geometry of free loci and factorization of noncommutative polynomials, Adv. Math. 331 (2018) 589-626 (arXiv, pdf)
26. I. Klep, Š. Špenko, J. Volčič: Positive trace polynomials and the universal Procesi-Schacher conjecture, Proc. London Math. Soc. 117 (2018) 1101-1134 (arXiv, pdf)
27. J. Volčič: Matrix coefficient realization theory of noncommutative rational functions, J. Algebra 499 (2018) 397-437 (arXiv, pdf)
28. M. Brešar, C. Hanselka, I. Klep, J. Volčič: Skolem-Noether algebras, J. Algebra 498 (2018) 294-314 (arXiv, pdf)
29. I. Klep, J. Povh, J. Volčič: Minimizer extraction in polynomial optimization is robust, SIAM J. Optim. 28 (2018) 3177-3207 (Optimization online, pdf)
30. I. Klep, J. Volčič: Free loci of matrix pencils and domains of noncommutative rational functions, Comment. Math. Helv. 92 (2017) 105-130 (arXiv, pdf)
31. I. Klep, J. E. Pascoe, J. Volčič: Regular and positive noncommutative rational functions, J. London Math. Soc. 95 (2017) 613-632 (arXiv, pdf)
32. J. Volčič: On domains of noncommutative rational functions, Linear Algebra Appl. 516 (2017) 69-81 (arXiv, pdf)
33. I. Klep, V. Vinnikov, J. Volčič: Null- and Positivstellensätze for rationally resolvable ideals, Linear Algebra Appl. 527 (2017) 260-293 (arXiv, pdf)
34. J. Volčič: Cyclic homology of truncated quiver algebras, J. Pure Appl. Algebra 219 (2015) 33-46

Preprints

1. E. Shamovich, J. Volčič: Global structure behind pointwise equivalences of noncommutative polynomials (pdf)
2. I. Klep, T. Štrekelj, J. Volčič: Quantum Max d-Cut via qudit swap operators (pdf)
3. S. R. Garcia, J. Volčič: A noncommutative generalization of Hunter's positivity theorem (pdf)
4. I. Klep, V. Magron, J. Volčič: Complete upper bound hierarchies for spectral minimum in noncommutative polynomial optimization (pdf)
5. M. Farkas, J. Volčič, S. A. L. Storgaard, R. Chen, L. Mančinska: Maximal device-independent randomness in every dimension (pdf)
6. M. Brešar, J. Volčič: Matrix evaluations of noncommutative rational functions and Waring problems (pdf)

Conferences

• International Workshop on Operator Theory and Applications, University of Twente, Netherlands, Jun 2025.
• NC function theory: The Non-Commutative Frontier of Analysis and Algebra, Banff International Research Station, Canada, May 2025.
• Mathematical Theory of Networks and Systems, University of Cambridge, United Kingdom, Aug 2024.
• International Workshop on Operator Theory and Applications, University of Canterbury, United Kingdom, Aug 2024.
• Joint Mathematics Meetings, San Francisco, California, Jan 2024.
• Combinatorics in Algebraic Structures: Invariant Theory and its Applications, online, Nov 2023.
• International Workshop on Operator Theory and Applications, University of Helsinki, Finland, Aug 2023.
• Rings and Factorizations, University of Graz (plenary talk), Austria, Jul 2023.
• Conference of the International Linear Algebra Society, Technical University of Madrid, Spain, Jun 2023.
• Real Algebraic Geometry with a View toward Koopman Operator Methods, Oberwolfach Research Institute for Mathematics, Germany, Mar 2023.
• Joint Spectra and related Topics in Complex Dynamics and Representation Theory, Banff International Research Station, Canada, May 2023.
• Mathematical Theory of Networks and Systems, University of Bayreuth, Germany, Sep 2022.
• International Workshop on Operator Theory and Applications, Jagiellonian University, Poland, Sep 2022.
• Quantum Geometry, University of the Faroe Islands, Faroe Islands, Jun 2022.
• Algebraic and Combinatorial Perspectives in the Mathematical Sciences, online, Jun 2022.
• International Workshop on Operator Theory and Applications (semiplenary talk), Lancaster University, United Kingdom, Aug 2021.
• International Workshop on Operator Theory and Applications, Chapman University California, Aug 2021.
• 8th European Congress of Mathematics, Portorož, Slovenia, Jun 2021.
• Noncommutative inequalities, American Institute of Mathematics, Jun 2021.
• 37th Southeastern Analysis Meeting (semiplenary talk), online, Mar 2021.
• Joint Mathematics Meetings, online, Jan 2021.
• The Online Operator Theory and Related Topics, online, Jun 2020.
• Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability, Oberwolfach Research Institute for Mathematics, Germany, Mar 2020.
• Joint Mathematics Meetings, Denver, Colorado, Jan 2020.
• AMS Southeastern Sectional Meeting, University of Florida, Florida, Nov 2019.
• Noncommutative Analysis, Computational Complexity, and Quantum Information, Harvard University, Massachusetts, Oct 2019.
• International Workshop on Operator Theory and Applications, University of Lisbon, Portugal, Jul 2019.
• SIAM Conference on Applied Algebraic Geometry, University of Bern, Switzerland, Jul 2019.
• Focus Program on Applications of Noncommutative Functions, Fields Institute, Canada, Jun 2019.
• Multivariable Spectral Theory and Representation Theory, Banff International Research Station, Canada, Apr 2019.
• International Workshop on Operator Theory and Applications, East China Normal University, China, Jul 2018.
• Mathematical Theory of Networks and Systems, The Hong Kong University of Science and Technology, Hong Kong, Jul 2018.
• Joint Mathematics Meetings, San Diego, California, Jan 2018.
• Multivariable Operator Theory, Technion, Israel, Jun 2017.
• Real Algebraic Geometry With a View Toward Moment Problems and Optimization, Oberwolfach Research Institute for Mathematics, Germany, Mar 2017.
• International Workshop on Operator Theory and Applications, Washington University in St. Louis, Missouri, Jul 2016.
• Conference of the International Linear Algebra Society, Catholic University of Leuven, Belgium, Jul 2016.
• New Zealand Mathematical Society Colloquium, University of Canterbury, New Zealand, Dec 2015.
• Noncommutative rings and their applications, University of Artois, France, Jun 2015.

Education