Assist. Prof. dr. Aljaž Zalar
Assistant Professor
E:Send a message
Room: R3.15 - Kabinet
Description

https://zalara.github.io/

Classes
Laboratory
Projects
Past projects
Publications
  1. with S. Yoo: Core Varieties of Moment Matrices with Low-Degree Column Relations, submitted.
  2. with I. Zobovič: The matricial univariate rational truncated moment problem, submitted.
  3. with M. Omladič, M. Vuk: A linear programming approach to finite copula interpolation, submitted.
  4. with R. Nailwal, I. Zobovič: Truncated moment problems and the extension property on monomial curves, submitted.
  5. with M. Filip: Unobstructedness of affine terminal gorenstein toric fourfolds, submitted.
  6. with A. Bhardwaj: A constructive approach to the truncated moment problem on cubic curves in Weierstrass form, submitted.
  7. with M. Kummer: Non-negative polynomials on generalized elliptic curves, submitted.
  8. with M. Kummer: Positive polynomials and the truncated moment problem on plane cubics.
  9. with R. Nailwal: Moment theory approach to Gaussian quadratures with prescribed nodes, submitted.
  10. with I. Zobovič: Matricial Gaussian quadrature rules: singular case, in revision in Linear and Multilinear Algebra.
  11. with L. Fialkow: The pure Y=Xd truncated moment problem: part 1, in revision in Advances in Operator Theory.
  12. with S. Yoo: Bivariate Truncated Moment Sequences with the Column Relation XY=Xm + q(X), with q of degree m-1, in revision in Linear and Multilinear Algebra.
  13. with M. Omladič, H. Radjavi, K. Šivic: Thick compressions of thin algebras, Linear Algebra Appl. 753 (2027) 273-298.
  14. with S. Yoo: Constructive approach to the truncated moment problem on reducible cubic curves: hyperbolic-type relations, Banach J. Math. Anal. 20, 44 (2026).
  15. with R. Nailwal: Cyclic polynomials in Dirichlet-type Spaces of the unit bidisk, Anal. Math. Phys. 16, 87 (2026).
  16. with M. Omladič, M. Vuk: Maximal signed volume for (multivariate) supermodular quasi-copulas, International Journal of Approximate Reasoning 197 (2026) 109748.
  17. with S. Sun: Matrix Fejér-Riesz type theorem for a union of an interval and a point, J. Pure Appl. Algebra 230 (2026) 108173.
  18. with M. Omladič, M. Vuk: Extreme mass distributions for quasi-copulas, Fuzzy Sets and Systems 527 (2026) 109698.
  19. with I. Zobovič: Matricial Gaussian quadrature rules: nonsingular case, Linear Algebra Appl. 731 (2026) 160-185.
  20. with I. Klep, K. Šivic: Cross-positive linear maps, sums of squares and positive polynomials, Journal of Algebra 688 (2026) 189-243.
  21. with T. Štrekelj: Construction of exceptional copositive matrices, Linear Algebra Appl. 727 (2025) 368-384.
  22. with M. Belšak, M. Omladič, M. Vuk: Extreme values of the mass distribution associated with d-quasi-copulas via linear programming, Fuzzy Sets and Systems 517 (2025) 109457.
  23. with R. Nailwal: The truncated univariate rational moment problem, Linear Algebra and its Applications 708 (2025) 280-301.
  24. with I. Klep, T. Štrekelj: A random copositive matrix is completely positive with positive probability, SIAM Journal on Applied Algebra and Geometry 8, 3 (2024) 583-611.
  25. with S. Yoo: The truncated moment problem on reducible cubic curves I: Parabolic and Circular type relations, Complex Anal. Oper. Theory 18, 111 (2024) 54 pp.
  26. The truncated moment problem on curves y=q(x) and yxℓ=1, Linear and Multilinear Algebra 72, 12 (2024) 1922-1966.
  27. The strong truncated Hamburger moment problem with and without gaps, J. Math. Anal. Appl. 516 (2022) 21 pp.
  28. The truncated moment problem on the union of parallel lines, Linear Algebra and its Applications 649 (2022) 186-239.
  29. The truncated Hamburger moment problems with gaps in the index set, Integ. Equ. Oper. Theory 93 (2021) 36 pp.
  30. with A. Bhardwaj: The tracial moment problem on quadratic varieties, J. Math. Anal. Appl. 498 (2021) 39 pp.
  31. with J. Cimprič: A local-global principle for linear dependence in enveloping algebras of Lie algebras, Linear Algebra and its Applications 596 (2020) 230-255.
  32. with I. Klep, S. McCullough, K. Šivic: There are many more positive maps than completely positive maps, Int. Math. Res. Not. 11 (2019) 3313-3375.
  33. with A. Bhardwaj: The singular bivariate quartic tracial moment problem, Complex Anal. Oper. Theory 12 (2018) 1057-1142.
  34. Operator Positivstellensätze for noncommutative polynomials positive on matrix convex sets, J. Math. Anal. Appl. 445 (2017) 32-80.
  35. Matrix Fejér-Riesz theorem with gaps, J. Pure Appl. Algebra 220 (2016) 2533-2548.
  36. Non-negative spectral measures and representations of C*-algebras, Integ. Equ. Oper. Theory 79 (2014) 219-242.
  37. with J. Cimprič: Moment problems for operator polynomials, J. Math. Anal. Appl. 401 (2013) 307-316.
  38. A note on a matrix version of the Farkas lemma, Comm. Algebra 40 (2012) 3420-3429.
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