Research:
Primary interest: preserver problems, graph cores, etc.
Current research involves Matrix Theory with an addition of the theory of Finite Fields, Algebraic Graph Theory (mainly Spectral and Chromatic Graph Theory), some Geometry, and some Mathematical Physics.
Submitted manuscripts
M. Orel, A family of non-Cayley cores based on vertex-transitive or strongly regular self-complementary graphs. Preprint available at arXiv.
Slides of talk presentations at conferences:
1) 8th European Congress of Mathematics
2) Combinatorial Designs and Codes
Journal publications and accepted manuscripts
A. Hujdurović, K. Kutnar, B. Kuzma, D. Marušič, Š. Miklavič, M. Orel, On intersection density of transitive groups of degree a product of two odd primes. Finite Fields Appl. 78 (2022), 101975. Published version available freely till January 15 2022. Preprint available at arXiv.
M. Orel, Nonstandard rank-one nonincreasing maps on symmetric matrices. Linear and Multilinear Algebra 67(2) (2019), 391-432. Available here. DOI: 10.1080/03081087.2017.1419456
M. Orel, On Minkowski space and finite geometry. J. Combin. Theory Ser. A. 148 (2017), 145-182. http://dx.doi.org/10.1016/j.jcta.2016.12.004
M. Orel, On generalizations of the Petersen and the Coxeter graph. Electron. J. Combin. 22(4) (2015), Paper #P.4.27. Available freely online.
M. Orel, Adjacency preservers on invertible hermitian matrices I. Linear Algebra Appl. 499 (2016), 99-128. http://dx.doi.org/10.1016/j.laa.2014.10.034
M. Orel, Adjacency preservers on invertible hermitian matrices II. Linear Algebra Appl. 499 (2016), 129-146. http://dx.doi.org/10.1016/j.laa.2014.10.033
M. Orel, Adjacency preservers, symmetric matrices, and cores, J. Algebraic Combin. 35 (4) (2012), 633-647. http://dx.doi.org/10.1007/s10801-011-0318-0
G. Dolinar, A. E. Guterman, B. Kuzma, M. Orel, On the Polya permanent problem over finite fields, European J. Combin. 32 (1) (2011), 116-132. http://dx.doi.org/10.1016/j.ejc.2010.07.001
M. Orel, B. Kuzma, Additive rank-one nonincreasing maps on hermitian matrices over the field GF(22), Electron. J. Linear Algebra 18 (2009), 482-499. Available freely online.
M. Orel, A note on adjacency preservers on hermitian matrices over finite fields, Finite Fields Appl. 15(4) (2009), 441-449. http://dx.doi.org/10.1016/j.ffa.2009.02.005
M. Orel, Nonbijective idempotents preservers over semirings, J. Korean Math. Soc. 47 (4) (2010), 805-818. Available freely online.
M. Orel, B. Kuzma, Additive maps on Hermitian matrices, Linear Multilinear Algebra 55 (6) (2007), 599-617. http://dx.doi.org/10.1080/03081080701265140
B. Kuzma, M. Orel, Additive mappings on symmetric matrices, Linear Algebra Appl. 418 (1) (2006), 277-291. http://dx.doi.org/10.1016/j.laa.2006.02.010
Chapters in books
M. Orel, Preserver problems over finite fields, in: J. Simmons (Ed.), Finite Fields: Theory, Fundamental Properties and Applications, Nova Science Publishers, New York, 2017, pp. 1-54.
(This chapter describes a connection between the study of preserver problems in matrix theory and the study of graph homomorphisms and cores in graph theory. It is written for mathematicians working in either of these two research areas. Graph theorists may find new motivation and applications for their research, while matrix theorists may find new techniques to solve preserver problems. Finally, the chapter surveys also some connections with finite geometry, where an increasing number of examples show that certain problems in finite geometry are related to the study of preserver problems and the study of graph homomorphisms.)
Proceedings
G. Dolinar, A. Guterman, B. Kuzma, and M. Orel. Permanent versus determinant over a finite field. Sovrem. Mat. Prilozh. Vol. 80, Proceedings of the International Conference ``Modern Algebra and Its Applications'' (Batumi, 2011), Part 1, 2012. English translation: J. Math. Sci. (N. Y.) 193 (3) (2013), 404-413. http://dx.doi.org/10.1007/s10958-013-1469-4