Scientific Papers
R. Kollár, Incomplete Finite Binomial Sums of Harmonic Numbers (2024), Journal of Integer Sequences 27, Article 24.2.1
K. Boďová, R. Kollár, M. Miglierini, Role of noise in human walking in the absence of orientational cues (2022), Physica D Nonlinear Phenomena 442 (5), 133535.
I. Kajanova, L. Lukacikova, L. Jelenska, K. Grossmannova, Z. Radikova, M. Vlcek, B. Klempa, R. Kollár, K. Bodova, J. Kopacek, S. Pastorekova, Seroprevalence of SARS-CoV-2 IgG antibodies in the staff of the Slovak Academy of Sciences in response to COVID-19 and/or vaccination: situation in August 2021 (2021), Acta Virologica 65 (4), 420-432.
K. Boďová, R. Kollár, Emerging algebraic growth trends in SARS-CoV-2 pandemic data (2020), Physical Biology 17 (6), 065012, arXiv
K. Boďová, R. Kollár, Spatial scales, patterns, and positivity trends of SARS-CoV-2 pandemics in mass rapid antigen testing in Slovakia (2021), PLoS ONE 16 (8), e0256669, medRxiv
R. Kollár, B. Deconinck, O. Tritchenko, Direct Characterization of Spectral Stability of Small Amplitude Periodic Waves in Scalar Hasmiltonian Problems via Dispersion Relation (2019), SIAM J. on Math Analysis 51 (4), 3145-3169, arXiv.
O. Tritchenko, B. Deconinck, R. Kollár, Stability of Periodic Traveling Wave Solutions to the Kawahara Equation (2018) SIAM Journal on Applied Dynamical Systems 17 (4), 2761-2783.
R. Kollár, S. Novak, Existence of Traveling Waves for the Generalized F–KPP Equation (2017), Bulletin of mathematical biology 79 (3), 525-559.
S. Novak, R. Kollár, Spatial Gene Frequency Waves Under Genotype-Dependent Dispersal (2017), Genetics 205, 1-9.
R. Kollár, K. Šišková, Extension and justification of quasi-steady-state approximation for reversible bimolecular binding (2015), Bulletin of mathematical biology 77 (7), 1401-1436.
K. Boďová, R. Kollár, J. Nosek, Ľ. Tomáška, Mathematical model of alternative mechanism of telomere length maintenance (2014), Phys. Rev. E 89, 032701, arxiv.
R. Bosák, R. Kollár, Index Theorems for Polynomial Pencils (2014). In Nonlinear Physical Systems. Spectral Analysis, Stability and Bifurcations, O. N. Kirillov and D. E. Pelinovsky eds., ISTE, London, pp. 177-202. arxiv
R. Kollár, P. D. Miller, Graphical Krein Signature Theory and Evans-Krein Functions (2014), SIAM Rev. 56 (1), 73–123. arxiv.
R. Kollár, Spectral stability of vortices in two-dimensional Bose-Einstein condensates via the Evans function and Krein signature (2012), Appl. Math. Res. Express 2012, 1-46, arXiv, 09-CNA-17 report.
R. Kollár, Homotopy Method for Nonlinear Eigenvalue Pencils with Applications (2011), SIAM J. Math. Anal. 43, 612-633.
R. Kollár, A. Scheel, Coherent structures generated by inhomogeneities in oscillatory media (2007), SIAM J. Appl. Dyn. Syst. 6, 236-262.
R. Kollár, Existence and Stability of Vortex Solutions of Certain Nonlinear Schrodinger Equations )2004), PhD. Thesis, University of Maryland.
K.F. Gurski, R. Kollár, R. L. Pego, Slow damping of internal waves in a stably stratified fluid (2004), Proc. R. Soc. Lond. A 460 (2044), 977-994.
M. Fečkan, R. Kollár, Discontinuous wave equations and a topological degree for some classes of multi-valued mapping (1999), Appl. Math. 44 (1), 15-32.
Textbooks, preprints, conference proceedings
R. Kollár, Matematické modelovanie v biológii (Mathematical modeling in biology). In Genomika (in Slovak language), J. Nosek et al., Charleston: CreateSpace Independent Publising, pp. 207-226 (2013).
K. Boďová, R. Kollár, Self-organization as absorbing Markov chain (2024), submitted.
R. Kollár, K. Boďová, True pandemic state and a lack of capacity of hospitals and mechanical ventilations in Slovakia during the SARS-CoV-2 pandemic wave in August 2020 - May 2021 (2021), Proceedings of the 21st Conference Information Technologies – Applications and Theory (ITAT 2021), 247-254
K. Boďová, V. Boža, B. Brejová, R. Kollár, K. Mikušová, T. Vinař, Time-adjusted analysis shows weak associations between BCG vaccination policy and COVID-19 disease progression (2021), Proceedings of the 21st Conference Information Technologies – Applications and Theory (ITAT 2021): 255-262, medRxiv
M. Šuster, K. Boďová, V. Nosáľ, R. Kollár, Determinants of COVID-19 hospitalizations in Slovakia (2021), Proceedings of the 21st Conference Information Technologies – Applications and Theory (ITAT 2021): 269-274
M. Medo, M. Suster, K. Bodova, A. Brazinova, B. Brejova, R. Kollár, V. Leksa, J. Lindbloom, J. Nosek, T. Vinar, Technical comment on The impact of population-wide rapid antigen testing on SARS-CoV-2 prevalence in Slovakia (2021), arXiv
Scientific Talks (2012-2023)
FMFI UK Seminar from qualitative theory of differential equations, Bratislava, Slovakia, March 14, 2024
ÖMG Tagung, Graz, Austria, September 19, 2023
FMFI UK Seminar from qualitative theory of differential equations, Bratislava, Slovakia, March 30, 2023
FMFI UK Seminar from qualitative theory of differential equations, Bratislava, Slovakia, November 4, 2021
University Washington, Applied Math Seminar (online), Seattle, WA, USA, October 7, 2021
ITAT Data Analysis in Response to Pandemics, Heľpa, Slovakia, September 28, 2021
FMFI UK Seminar from qualitative theory of differential equations, Bratislava, Slovakia, December 17, 2020
University Queensland, SMP Pandemic Seminar Group (online), Brisbane, Australia, May 25, 2020
The 11th IMACS International Conference, Nonlinear Evolution Equations and Wave Phenomena, Athens, GA, USA, April 17-19, 2019
Analysis and PDE Seminar, Michigan State University, Lansing, MI, USA, September 19, 2018
Erwin Schrodinger Institute, Nonlinear Water Waves - an Interdisciplinary Interface Workshop, December 2017
The 10th IMACS International Conference, Nonlinear Evolution Equations and Wave Phenomena, Athens, GA, USA, March 2017
Analysis Seminar, Masarykova Univerzita, Brno, Czech Republic, October 17, 2016
SIAM Conference on Nonlinear Waves and Coherent Structures, Cambridge, UK, August 11-14, 2014
AIMS Conference on Dynamical Systems, Diff. Eqs. and Appl., Madrid, Spain, July 7-11, 2014
Applied and Interdisciplinary Mathematics seminar, U Michigan, Ann Arbor, USA, November 22, 2013
Workshop Numerical analysis of equivariant evolution equations, Bielefeld, Germany, June 19, 2013
SIAM Conference on Dynamical Systems, Snowbird, UT, USA, May 19-23, 2013
Analysis Seminar, University of Missouri, Columbia, MO, USA, November 15, 2012
Popular Science Talks (2012-2023) See Media page for live footage of some of the talks
FMFI UK (Popular science public lecture), Introductory Week for New Students, Bratislava, Slovakia, September 13, 2023
FMFI UK Open Doors Day (Popular science public lecture), Bratislava, Slovakia, June 8, 2022
Conference Právne, forenzné a ekomonické aspekty medicíny, Bratislava, Slovakia, September 25, 2021
Viva la science! (Popular science public lecture), Summer School University of Agriculture, Nitra, Slovakia, August 21, 2021
Bratislava International School of Liberal Arts, May 20, 2021
Presentation for Slovenská spoločnosť aktuárov (online), March 17, 2021
Veda v centre (Popular science public lecture), Slovak Centre of Scientific and Technical Information, Bratislava, Slovakia, February 26, 2021
Conference Právne, forenzné a ekomonické aspekty medicíny, Bratislava, Slovakia, December 9, 2020
Rotary Club, Bratislava, Slovakia, November 9, 2020
Večer zvedavých (Popular science public lecture), Bratislava, Slovakia, October 14, 2020
Tabuľa (Popular science public lecture) Slovak Academy of Sciences, Bratislava, Slovakia, April 29, 2020
Trojsten Academy (Popular science public lecture), Bratislava, Slovakia, December 7, 2018
Vedatour (Popular science public lecture), Bratislava, Slovakia, October 25, 2018
DNA Days (Popular science public lecture), KC Dunaj, Bratislava, Slovakia, April 23, 2018
Plenary talk at the Student Scientific Conference, comenius University, Bratislava, SK, April 23, 2014