Dušan Repovš
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Dušan D. Repovš (born November 30, 1954) is a Slovenian mathematician from
Ljubljana Ljubljana (also known by other historical names) is the capital and largest city of Slovenia. It is the country's cultural, educational, economic, political and administrative center. During antiquity, a Roman city called Emona stood in the are ...
, Slovenia. He graduated in 1977 from the
University of Ljubljana The University of Ljubljana ( sl, Univerza v Ljubljani, , la, Universitas Labacensis), often referred to as UL, is the oldest and largest university in Slovenia. It has approximately 39,000 enrolled students. History Beginnings Although certain ...
. He obtained his PhD in 1983 from Florida State University with thesis ''Generalized Three-Manifolds with Zero-Dimensional Singular Set'' written under the direction of Robert Christopher Lacher. He held a fellowship from the Research Council of Slovenia and a Fulbright scholarship. In 1993 he was promoted to Professor of
Geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...
and
Topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
at the University of Ljubljana, where he is employed at the Faculty of Mathematics and Physics and at the Faculty of Education, as the Head of the Chair for Geometry and Topology. Since 1983 he has been the leader of the Slovenian Nonlinear Analysis, Topology and Geometry Group at the Institute of Mathematics, Physics and Mechanics in Ljubljana, and has directed numerous national and international research grants (with the United States, Japan, Russian Federation, China, France, Italy, Spain, Israel, United Kingdom, Poland, Hungary, Romania, Slovakia, and others). The Slovenian Research Agency has selected this group among the best research program groups in Slovenia. Repovš is the leading Slovenian expert on
nonlinear analysis Nonlinear functional analysis is a branch of mathematical analysis that deals with nonlinear mappings. Topics Its subject matter includes: * generalizations of calculus to Banach spaces * implicit function theorems * fixed-point theorems (Br ...
and
topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
and is one of the best known Slovenian mathematicians. He has published over 450 research papers and has given numerous invited talks at various international conferences and universities around the world. His research interests are in
nonlinear analysis Nonlinear functional analysis is a branch of mathematical analysis that deals with nonlinear mappings. Topics Its subject matter includes: * generalizations of calculus to Banach spaces * implicit function theorems * fixed-point theorems (Br ...
and its applications,
topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
, and
algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...
. He first became known in the 1980s for his results in geometric topology, notably the solution of the classical recognition problem for
3-manifolds In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane to a small enough observer, all 3-manifolds ...
, the proof of the 4-dimensional Cellularity Criterion, and the proof of the Lipschitz case of the classical Hilbert–Smith conjecture. Presently he is most actively investigating in nonlinear analysis.N. S. Papageorgiou, V. D. Radulescu and D. D. Repovš, Nonlinear Analysis – Theory and Methods, Springer, Cham 2019
MR3890060
Later he extended his research to several other areas and is currently most actively investigating problems of
partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...
. He covers a very broad spectrum: problems with nonstandard growth (variable exponents, anisotropic problems, double-phase problems), qualitative analysis of solutions of semilinear and quasilinear PDEs (Dirichlet, Neumann, Robin boundary conditions), singular and degenerate problems (blow-up boundary, singular reactions), inequality problems (variational, hemivariational, both either stationary or evolutionary). His analysis of these problems combines fine methods at the interplay between nonlinear functional analysis, critical point theory, variational, topological and analytic methods, mathematical physics, and others. He has published a monograph on nonlinear analysis, a monograph on partial differential equations with variable exponents, a monograph on continuous selections of multivalued mappings, and a monograph on higher-dimensional generalized manifolds, as well as also a university textbook on topology. He is serving on the editorial boards of the
Journal of Mathematical Analysis and Applications The ''Journal of Mathematical Analysis and Applications'' is an academic journal in mathematics, specializing in mathematical analysis and related topics in applied mathematics. It was founded in 1960, as part of a series of new journals on areas o ...
, Advances in Nonlinear Analysis, Boundary Value Problems, Complex Variables and Elliptic Equations, and others. For his outstanding research he was awarded in 2014 the honorary doctorate by the
University of Craiova The University of Craiova ( ro, Universitatea din Craiova) is a public university located in Craiova, Romania. It was founded in 1947, initially with four institutes, in the Palace of Justice of Craiova. It is the largest university in the histori ...
, in 2009 the
Bogolyubov Bogolyubov or Boholyubov (; ) is a surname in Russia and Ukraine, meaning "he who loves God" or, possibly "he who is loved by God". Spellings Bogoljubov and Bogoliubov are also used. The feminine form is Bogolyubova (russian: Боголюбова). ...
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
European Academy of Sciences and Arts The European Academy of Sciences and Arts (EASA, la, Academia Scientiarum et Artium Europaea) is a transnational and interdisciplinary network, connecting about 2,000 recommended scientists and artists worldwide, including 37 Nobel Prize laur ...
, the
New York Academy of Sciences The New York Academy of Sciences (originally the Lyceum of Natural History) was founded in January 1817 as the Lyceum of Natural History. It is the fourth oldest scientific society in the United States. An independent, nonprofit organization wi ...
, the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
, the
European Mathematical Society The European Mathematical Society (EMS) is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians. The current ...
, the London Mathematical Society, the
Mathematical Society of Japan The Mathematical Society of Japan (MSJ, ja, 日本数学会) is a learned society for mathematics in Japan. In 1877, the organization was established as the ''Tokyo Sugaku Kaisha'' and was the first academic society in Japan. It was re-organized ...
, the
Moscow Mathematical Society The Moscow Mathematical Society (MMS) is a society of Moscow mathematicians aimed at the development of mathematics in Russia. It was created in 1864, and Victor Vassiliev is the current president. History The first meeting of the society wa ...
, the French Mathematical Society, the
Swiss Mathematical Society The Swiss Mathematical Society (german: Schweizerische Mathematische Gesellschaft; french: Société Mathématique Suisse), founded in Basel on September 4, 1910, is the national mathematical society of Switzerland and a member society of the Europ ...
, and others. He is also a founding member of the Slovenian Engineering Academy.


Notes

{{DEFAULTSORT:Repovs, Dusan 21st-century Slovenian mathematicians Topologists Florida State University alumni 1954 births Living people University of Ljubljana alumni Academic staff of the University of Ljubljana Scientists from Ljubljana Members of the European Academy of Sciences and Arts PDE theorists 20th-century Slovenian mathematicians Fulbright alumni