|Dušan D. Repovš|
November 30, 1954 |
|Alma mater||Florida State University
University of Ljubljana
He graduated in 1977 from the University of Ljubljana with a thesis on the Borsuk shape theory. He obtained his Ph.D. in 1983 at the Florida State University with a dissertation on generalized 3-manifolds with 0-dimensional singular set. During his studies at the University of Ljubljana he had a fellowship from the Research Council of Slovenia, and he went to the United States on a Fulbright grant.
In 1993 he was promoted to a Professor of Geometry and Topology at the University of Ljubljana, where he is employed at the Faculty of Education, as the Head of the Chair for Geometry and Topology, and at the Faculty of Mathematics and Physics. Since 1983 he has also been the Head of the Slovenian Topology, Geometry and Nonlinear Analysis Group at the Institute of Mathematics, Physics and Mechanics in Ljubljana, and has directed numerous national and international research grants (with United States, Japan, Russian Federation, China, France, Italy, Spain, Israel, United Kingdom, Poland, Hungary, Romania, Slovakia, and others). The Slovenian Research Agency has selected his group among the best research program groups in Slovenia.
Professor Repovš is the leading Slovenian expert on topology and nonlinear analysis and is one of the best known Slovenian mathematicians. He has published over 340 research papers and has given over 400 invited talks at various international conferences and universities around the world.
His research areas are mostly set theory, topology, algebra and nonlinear analysis. He is best known for his work in geometric topology, notably the solution of the classical recognition problem for 3-manifolds, the proof of the 4-dimensional Cellularity Criterion, and the proof of the Lipschitz case of the classical Hilbert–Smith Conjecture. Later he extended his research to several other areas and is currently most actively investigating problems on partial differential equations.
He has published a monograph on continuous selections of multivaled mappings  , a monograph on partial differential equations with variable exponents , a monograph on higher-dimensional generalized manifolds, and a university textbook on topology.
For his outstanding research he was awarded in 2014 the Honorary Doctorate by the University of Craiova , in 2009 the Bogolyubov Memorial Medal by the Ukrainian Mathematical Congress in Kiev and in 1997 the Prize of the Republic of Slovenia for Research (now called the Zois Prize). For his promotion of the Slovenian science abroad he received in 1995 the honorary title of the Ambassador for Science of the Republic of Slovenia. He is a member of the New York Academy of Sciences, the American Mathematical Society, the European Mathematical Society, the London Mathematical Society, the Mathematical Society of Japan, the Moscow Mathematical Society, the French Mathematical Society, the Swiss Mathematical Society, and others. He is also a founding member of the Slovenian Engineering Academy .
- R. J. Daverman and D. Repovš, A new 3-dimensional shrinking criterion, Trans. Amer. Math. Soc. 315:1 (1989), 219-230, MR978381.
- D. Repovš, A criterion for cellularity in a topological 4-manifold, Proc. Amer. Math. Soc. 100:3 (1987), 564-566, MR891164.
- D. Repovš and E. V. Ščepin, A proof of the Hilbert-Smith conjecture for actions by Lipschitz maps, Math. Ann. 308:2 (1997), 361-364, MR1464908.
- D. Repovš, Asymptotics for singular solutions of the quasilinear logistic equation with absorption term, J. Math. Anal. Appl. 395:1 (2012), 78-85, MR2943604.
- V. D. Radulescu and D. D. Repovš, Partial Differential Equations with Variable Exponents, Chapman and Hall/CRC, Taylor & Francis Group, Boca Raton, FL, 2015, MR3379920.
- D. Repovš and P. V. Semenov, Continuous Selections of Multivalued Mappings, Kluwer Academic Publishers, Dordrecht 1998, MR1659914.
- A. Cavicchioli, F. Hegenbarth and D. Repovš, Higher-Dimensional Generalized Manifolds: Surgery and Constructions, European Mathematical Society, Zürich 2016, ZB06584147.
- M. Cencelj and D. Repovš, Topology (in Slovenian), Faculty of Education, University of Ljubljana, 2001.