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.

Contact

Research interests

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

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Published and accepted papers

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

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