Jurij Volčič

Contact

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Current position (Aug 2018 - ): Visiting Assistant Professor, Department of Mathematics, Texas A&M University

Past position (Nov 2017 - Aug 2018): Postdoctoral Fellow, Department of Mathematics, Ben-Gurion University of the Negev

Research interests

Free analysis, free real algebraic geometry, invariant theory, noncommutative rational functions, representation theory, skew fields.

Teaching

Published and accepted papers

  1. J. W. Helton, I. Klep, S. McCullough, J. Volčič: Noncommutative polynomials describing convex sets, Found. Comput. Math. (2020) (arXiv, pdf)
  2. 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)
  3. I. Klep, V. Vinnikov, J. Volčič: Multipartite rational functions, accepted in Doc. Math. (pdf)
  4. 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)
  5. J. W. Helton, I. Klep, J. Volčič: Factorization of noncommutative polynomials and Nullstellensätze for the free algebra, Int. Math. Res. Not. (2020) (arXiv, pdf)
  6. J. Volčič: Free Bertini's theorem and applications, Proc. Amer. Math. Soc. 148 (2020) 3661-3671 (arXiv, pdf)
  7. 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)
  8. I. Klep, J. Volčič: A note on group representations, determinantal hypersurfaces and their quantizations, to appear in Operator Theory, Functional Analysis and Applications, Oper. Theory Adv. Appl. 282, Birkhäuser/Springer, Cham, 2020 (pdf)
  9. 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)
  10. J. Volčič: Stable noncommutative polynomials and their determinantal representations, SIAM J. Appl. Algebra Geometry 3 (2019) 152–171 (arXiv, pdf)
  11. J. W. Helton, I. Klep, J. Volčič: Geometry of free loci and factorization of noncommutative polynomials, Adv. Math. 331 (2018) 589-626 (arXiv, pdf)
  12. 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)
  13. J. Volčič: Matrix coefficient realization theory of noncommutative rational functions, J. Algebra 499 (2018) 397-437 (arXiv, pdf)
  14. M. Brešar, C. Hanselka, I. Klep, J. Volčič: Skolem-Noether algebras, J. Algebra 498 (2018) 294-314 (arXiv, pdf)
  15. I. Klep, J. Povh, J. Volčič: Minimizer extraction in polynomial optimization is robust, SIAM J. Optim. 28 (2018) 3177–3207 (Optimization online, pdf)
  16. I. Klep, J. Volčič: Free loci of matrix pencils and domains of noncommutative rational functions, Comment. Math. Helv. 92 (2017) 105-130 (arXiv, pdf)
  17. I. Klep, J. E. Pascoe, J. Volčič: Regular and positive noncommutative rational functions, J. London Math. Soc. 95 (2017) 613-632 (arXiv, pdf)
  18. J. Volčič: On domains of noncommutative rational functions, Linear Algebra Appl. 516 (2017) 69–81 (arXiv, pdf)
  19. I. Klep, V. Vinnikov, J. Volčič: Null- and Positivstellensätze for rationally resolvable ideals, Linear Algebra Appl. 527 (2017) 260–293 (arXiv, pdf)
  20. J. Volčič: Cyclic homology of truncated quiver algebras, J. Pure Appl. Algebra 219 (2015) 33–46

Submitted papers

  1. I. Klep, V. Magron, J. Volčič: Optimization over trace polynomials (pdf)
  2. I. Klep, J. E. Pascoe, J. Volčič: Positive univariate trace polynomials (pdf)

Reports

  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) (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