Jurij Volčič

Real algebraic geometry, free analysis, noncommutative algebra, invariant theory, quantum information, polynomial optimization.


Experience

Assistant Professor

Department of Mathematics, Drexel University, Pennsylvania
Sep 2022 - Present

Postdoc

Department of Mathematical Sciences, University of Copenhagen, Denmark
Sep 2021 - Aug 2022

Visiting Assistant Professor

Department of Mathematics, Texas A&M University, Texas
Aug 2018 - Aug 2021

Postdoctoral Fellow

Department of Mathematics, Ben-Gurion University of the Negev, Israel
Nov 2017 - Aug 2018

PhD Candidate, Teaching Assistant

Department of Mathematics, University of Auckland, New Zealand
Oct 2014 - Sep 2017

Research

Published papers

  1. H. Derksen, I. Klep, V. Makam, J. Volčič: Ranks of linear matrix pencils separate simultaneous similarity orbits, Adv. Math. 415 (2023) 108888 (arXiv, pdf)
  2. I. Klep, C. Scheiderer, J. Volčič: Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem, Math. Ann. (2022) (arXiv, pdf)
  3. 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)
  4. 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)
  5. 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)
  6. I. Klep, V. Magron, J. Volčič: Optimization over trace polynomials, Ann. Henri Poincaré 23 (2022) 67-100 (arXiv, pdf)
  7. J. W. Helton, I. Klep, S. McCullough, J. Volčič: Noncommutative polynomials describing convex sets, Found. Comput. Math. 21 (2021) 575-611 (arXiv, pdf)
  8. I. Klep, J. E. Pascoe, J. Volčič: Positive univariate trace polynomials, J. Algebra 579 (2021) 303-317 (arXiv, pdf)
  9. J. Volčič: Hilbert's 17th problem in free skew fields, Forum Math. Sigma 9 (2021) E61 (arXiv, pdf)
  10. 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)
  11. I. Klep, V. Vinnikov, J. Volčič: Multipartite rational functions, Doc. Math. 25 (2020) 1285-1313 (arXiv, pdf)
  12. 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)
  13. J. Volčič: Free Bertini's theorem and applications, Proc. Amer. Math. Soc. 148 (2020) 3661-3671 (arXiv, pdf)
  14. 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)
  15. 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)
  16. 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)
  17. J. Volčič: Stable noncommutative polynomials and their determinantal representations, SIAM J. Appl. Algebra Geometry 3 (2019) 152–171 (arXiv, pdf)
  18. J. W. Helton, I. Klep, J. Volčič: Geometry of free loci and factorization of noncommutative polynomials, Adv. Math. 331 (2018) 589-626 (arXiv, pdf)
  19. 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)
  20. J. Volčič: Matrix coefficient realization theory of noncommutative rational functions, J. Algebra 499 (2018) 397-437 (arXiv, pdf)
  21. M. Brešar, C. Hanselka, I. Klep, J. Volčič: Skolem-Noether algebras, J. Algebra 498 (2018) 294-314 (arXiv, pdf)
  22. I. Klep, J. Povh, J. Volčič: Minimizer extraction in polynomial optimization is robust, SIAM J. Optim. 28 (2018) 3177–3207 (Optimization online, pdf)
  23. I. Klep, J. Volčič: Free loci of matrix pencils and domains of noncommutative rational functions, Comment. Math. Helv. 92 (2017) 105-130 (arXiv, pdf)
  24. I. Klep, J. E. Pascoe, J. Volčič: Regular and positive noncommutative rational functions, J. London Math. Soc. 95 (2017) 613-632 (arXiv, pdf)
  25. J. Volčič: On domains of noncommutative rational functions, Linear Algebra Appl. 516 (2017) 69–81 (arXiv, pdf)
  26. I. Klep, V. Vinnikov, J. Volčič: Null- and Positivstellensätze for rationally resolvable ideals, Linear Algebra Appl. 527 (2017) 260–293 (arXiv, pdf)
  27. J. Volčič: Cyclic homology of truncated quiver algebras, J. Pure Appl. Algebra 219 (2015) 33-46

Preprints

  1. R. Chen, J. Volčič, L. Mančinska: All projective measurements can be self-tested (pdf)
  2. I. Klep, V. Macron, J. Volčič, J. Wang: State polynomials: positivity, optimization and nonlinear Bell inequalities (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) 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)

Talks

  • Mathematical Theory of Networks and Systems, University of Bayreuth, Germany, Sep 2022.
  • International Workshop on Operator Theory and Applications, Jagiellonian University, Poland, Sep 2022.
  • Algebraic and Combinatorial Perspectives in the Mathematical Sciences, online, Jun 2022.
  • International Workshop on Operator Theory and Applications (semiplenary talk), Lancaster University, UK, 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, Mathematisches Forschungsinstitut Oberwolfach, 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, Mathematisches Forschungsinstitut Oberwolfach, 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, Katholieke Universiteit 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

Doctor of Philosophy in Math (Mar 2018)

Faculty of Science, University of Auckland, New Zealand

Thesis: Noncommutative rational functions and their finite dimensional representations.
Supervisor: Igor Klep.

Oct 2014 - Sep 2017

Master in Math

Faculty of Mathematics and Physics, University of Ljubljana, Slovenia

Thesis: Homological properties of truncated quiver algebras.
Supervisor: Matjaž Omladič.

Oct 2012 - Jul 2014

Bachelor in Math

Faculty of Mathematics and Physics, University of Ljubljana, Slovenia

Thesis: Hochschild cohomology of algebra related to oriented cycle.
Supervisor: Matjaž Omladič.

Oct 2009 - Sep 2012