Aljaž Zalar

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University of Ljubljana
Faculty for Computer and Information Science
Personal website
Večna pot 113, 1000 Ljubljana, Slovenia

e-mail: aljaz.zalar@fri.uni-lj.si

Research interests

Real algebraic geometry, truncated moment problems, moment problems, matrix polynomials, completely positive maps.

Preprints

  1. with R. Nailwal: The truncated univariate rational moment problem
  2. with M. Belšak, M. Omladič, M. Vuk: Extreme values of the mass distribution associated with d-quasi-copulas via linear programming
  3. with I. Klep, K. Šivic: Cross-positive linear maps, sums of squares and positive polynomials

Publications

  1. 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. (pdf)
  2. 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. (pdf)
  3. The truncated moment problem on curves y=q(x) and yx^ℓ=1, Linear and Multilinear Algebra 72, 12 (2024) 1922-1966. (pdf)
  4. The strong truncated Hamburger moment problem with and without gaps, J. Math. Anal. Appl. 516 (2022) 21 pp. (pdf)
  5. The truncated moment problem on the union of parallel lines, Linear Algebra and its Applications 649 (2022) 186--239. (pdf)
  6. The truncated Hamburger moment problems with gaps in the index set, Integ. Equ. Oper. Theory 93 (2021) 36 pp. (pdf)
  7. with A. Bhardwaj: The tracial moment problem on quadratic varieties, J. Math. Anal. Appl. 498 (2021) 39 pp. (pdf)
  8. 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. (pdf)
  9. 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. (pdf)
  10. with A. Bhardwaj: The singular bivariate quartic tracial moment problem, Complex Anal. Oper. Theory 12 (2018) 1057-1142. (pdf)
  11. Operator Positivstellensätze for noncommutative polynomials positive on matrix convex sets, J. Math. Anal. Appl. 445 (2017) 32-80. (pdf)
  12. Matrix Fejér-Riesz theorem with gaps, J. Pure Appl. Algebra 220 (2016) 2533-2548. (pdf)
  13. Non-negative spectral measures and representations of C*-algebras, Integ. Equ. Oper. Theory 79 (2014) 219-242. (pdf)
  14. with J. Cimprič: Moment problems for operator polynomials, J. Math. Anal. Appl. 401 (2013) 307-316. (pdf)
  15. A note on a matrix version of the Farkas lemma, Comm. Algebra 40 (2012) 3420-3429. (pdf)

In preparation

  • with S. Yoo: Bivariate Truncated Moment Sequences with the Column Relation XY=X^m + q(X) and q of degree m-1.
  • with M. Kummer: Positive polynomials and the truncated moment problem on plane cubics.
  • with A. Bhardwaj: Flat extensions for cubic curves in Weierstrass form.
  • with S. Yoo: The truncated moment problem on reducible cubic curves II: Hyperbolic type relations.
  • with I. Klep, T. Štrekelj: Construction of exceptional copositive matrices

Talks

Teaching

  • Numerical Methods: 2019/20-24/25, Lecture notes (in Slovene)
  • Principles of Uncertainty (1/2): 2022/23-24/25
  • Mathematics 2 - MCMC methods (1/4): 2022/23-24/25

Previous teaching

Student supervision

Postdoctoral fellows

  • Rajkamal Nailwal, Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia, Nov 2024-

Master Thesis

Bachelor Thesis

Academic education