He graduated in 1977 from the University of Ljubljana with a thesis on the Borsuk shape theory. He obtained his Doctor of Philosophy 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 with 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, France, Italy, Spain, Israel, Poland, Hungary, Romania, Slovakia, and others).
The Slovenian Research Agency has selected this group among the best research program groups in Slovenia.
Professor Repovš is the leading Slovenian expert in topology and nonlinear analysis and is one of the best known mathematicians from Slovenia abroad. He has published over 300 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 of partial differential equations.
He published a monograph on continuous selections of multivaled mappings, a monograph on partial differential equations with variable exponents, and a university textbook on topology. Foreign 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 member of the Slovenian Engineering Academy.
