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 Postal address: Department of Mathematics Texas A&M University TAMU 3368 College Station TX 77843-3368 Email:volcic at math dot tamu dot edu 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. (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, Doc. Math. 25 (2020) 1285-1313 (arXiv, 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) rnaa122 (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. J. Volčič: Hilbert's 17th problem in free skew fields (pdf)
2. I. Klep, V. Magron, J. Volčič: Optimization over trace polynomials (pdf)
3. 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

• International Workshop on Operator Theory and Applications (semiplenary talk), Lancaster University, UK, August 2021.
• 8th European Congress of Mathematics, Portorož, Slovenia, June 2021.
• Noncommutative inequalities, American Institute of Mathematics (online), June 2021.
• 37th Southeastern Analysis Meeting (semiplenary talk), online, March 2021.
• Joint Mathematics Meetings, online, January 2021.
• The Online Operator Theory and Related Topics, online, June 2020.
• Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability, Mathematisches Forschungsinstitut Oberwolfach, Germany, March 2020.
• Joint Mathematics Meetings, Denver, Colorado, January 2020.
• AMS Southeastern Sectional Meeting, University of Florida, Florida, November 2019.
• Noncommutative Analysis, Computational Complexity, and Quantum Information, Harvard University, Massachusetts, October 2019.
• International Workshop on Operator Theory and Applications, University of Lisbon, Portugal, July 2019.
• SIAM Conference on Applied Algebraic Geometry, University of Bern, Switzerland, July 2019.
• Focus Program on Applications of Noncommutative Functions, Fields Institute, Canada, June 2019.
• Multivariable Spectral Theory and Representation Theory, Banff International Research Station, Canada, April 2019.
• International Workshop on Operator Theory and Applications, East China Normal University, China, July 2018.
• Mathematical Theory of Networks and Systems, The Hong Kong University of Science and Technology, Hong Kong, July 2018.
• Joint Mathematics Meetings, San Diego, California, January 2018.
• Multivariable Operator Theory, Technion, Israel, June 2017.
• Real Algebraic Geometry With a View Toward Moment Problems and Optimization, Mathematisches Forschungsinstitut Oberwolfach, Germany, March 2017.
• International Workshop on Operator Theory and Applications, Washington University in St. Louis, Missouri, July 2016.
• Conference of the International Linear Algebra Society, Katholieke Universiteit Leuven, Belgium, July 2016.
• New Zealand Mathematical Society Colloquium, University of Canterbury, New Zealand, December 2015.
• Noncommutative rings and their applications, University of Artois, France, June 2015.

Academic education

• 2014 - 2017: PhD in Mathematics, University of Auckland. Thesis: Noncommutative rational functions and their finite dimensional representations. Supervisor: Prof. Igor Klep.
• 2012 - 2014 : MSc in Mathematics, University of Ljubljana. Thesis: Homological properties of truncated quiver algebras. Supervisor: Prof. Matjaž Omladič.
• 2009 - 2012 : BSc in Mathematics, University of Ljubljana. Thesis: Hochschild cohomology of algebra related to oriented cycle. Supervisor: Prof. Matjaž Omladič.