Jurij Volčič

Current position: Visiting Assistant Professor, Department of Mathematics, Texas A&M University.

Past position: Postdoctoral Fellow, Department of Mathematics, Ben-Gurion University of the Negev.


Research interests

Noncommutative real algebraic geometry, free analysis, invariant theory, noncommutative rational functions, representation theory, skew fields, polynomial optimization.


Published and accepted papers

  1. J. W. Helton, I. Klep, S. McCullough, J. Volčič: Noncommutative polynomials describing convex sets, Found. Comput. Math. 21 (2021) 575-611 (arXiv, pdf)
  2. I. Klep, J. E. Pascoe, J. Volčič: Positive univariate trace polynomials, J. Algebra 579 (2021) 303-317 (arXiv, pdf)
  3. 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)
  4. I. Klep, V. Vinnikov, J. Volčič: Multipartite rational functions, Doc. Math. 25 (2020) 1285-1313 (arXiv, pdf)
  5. 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)
  6. J. W. Helton, I. Klep, J. Volčič: Factorization of noncommutative polynomials and Nullstellensätze for the free algebra, Int. Math. Res. Not. (2020) rnaa122 (arXiv, pdf)
  7. J. Volčič: Free Bertini's theorem and applications, Proc. Amer. Math. Soc. 148 (2020) 3661-3671 (arXiv, pdf)
  8. 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)
  9. 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)
  10. 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)
  11. J. Volčič: Stable noncommutative polynomials and their determinantal representations, SIAM J. Appl. Algebra Geometry 3 (2019) 152–171 (arXiv, pdf)
  12. J. W. Helton, I. Klep, J. Volčič: Geometry of free loci and factorization of noncommutative polynomials, Adv. Math. 331 (2018) 589-626 (arXiv, pdf)
  13. 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)
  14. J. Volčič: Matrix coefficient realization theory of noncommutative rational functions, J. Algebra 499 (2018) 397-437 (arXiv, pdf)
  15. M. Brešar, C. Hanselka, I. Klep, J. Volčič: Skolem-Noether algebras, J. Algebra 498 (2018) 294-314 (arXiv, pdf)
  16. I. Klep, J. Povh, J. Volčič: Minimizer extraction in polynomial optimization is robust, SIAM J. Optim. 28 (2018) 3177–3207 (Optimization online, pdf)
  17. I. Klep, J. Volčič: Free loci of matrix pencils and domains of noncommutative rational functions, Comment. Math. Helv. 92 (2017) 105-130 (arXiv, pdf)
  18. I. Klep, J. E. Pascoe, J. Volčič: Regular and positive noncommutative rational functions, J. London Math. Soc. 95 (2017) 613-632 (arXiv, pdf)
  19. J. Volčič: On domains of noncommutative rational functions, Linear Algebra Appl. 516 (2017) 69–81 (arXiv, pdf)
  20. I. Klep, V. Vinnikov, J. Volčič: Null- and Positivstellensätze for rationally resolvable ideals, Linear Algebra Appl. 527 (2017) 260–293 (arXiv, pdf)
  21. J. Volčič: Cyclic homology of truncated quiver algebras, J. Pure Appl. Algebra 219 (2015) 33-46

Submitted papers

  1. J. Volčič: Hilbert's 17th problem in free skew fields (pdf)
  2. I. Klep, V. Magron, J. Volčič: Optimization over trace polynomials (pdf)
  3. K. Aguilar, Á. Chávez, S. R. Garcia, J. Volčič: Norms on complex matrices induced by complete homogeneous symmetric polynomials (pdf)


  1. J. Volčič: Free real algebraic geometry, with a focus on convexity, in Real algebraic geometry with a view toward hyperbolic programming and free probability, Oberwolfach Rep. 12 (2020) 687-689 (pdf)
  2. J. Volčič: Real free loci of linear matrix pencils, in Real algebraic geometry with a view toward moment problems and optimization, Oberwolfach Rep. 14 (2017) 844-846 (pdf)

Conference talks

Academic education