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Projects / Programmes source: ARRS

Nestandardne vložitve Cantorjeve množice v Evklidski 3-prostor (Slovene)

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Research activity

Code Science Field Subfield
1.01.02  Natural sciences and mathematics  Mathematics  Topology 

Code Science Field
1.01  Natural Sciences  Mathematics 
Evaluation (rules)
source: COBISS
Citations Citations for bibliographic records in COBIB.SI that are linked to records in citation databases
source: WoS source: Scopus source: COBISS
Researchers (22)
no. Code Name and surname Research area Role Period No. of publications
1.  31193  PhD Taras Banakh  Natural sciences and mathematics  Researcher  2009 - 2012  322 
2.  30821  Andraž Briški-Javor  Natural sciences and mathematics  Junior researcher  2009  0 
3.  03342  PhD Matija Cencelj  Natural sciences and mathematics  Researcher  2009 - 2012  217 
4.  28252  PhD Dikran Dikranian  Natural sciences and mathematics  Researcher  2009 - 2012  205 
5.  29583  PhD Aleksandra Franc  Natural sciences and mathematics  Junior researcher  2009 - 2012  30 
6.  25594  PhD Gregor Jerše  Natural sciences and mathematics  Junior researcher  2009  27 
7.  32025  PhD Sara Kališnik  Natural sciences and mathematics  Junior researcher  2011 - 2012  16 
8.  34563  Peter Lendero  Natural sciences and mathematics  Junior researcher  2012  0 
9.  05485  PhD Jože Malešič  Natural sciences and mathematics  Researcher  2009  224 
10.  08947  PhD Nežka Mramor Kosta  Natural sciences and mathematics  Researcher  2009 - 2012  206 
11.  04588  PhD Dušan Pagon  Natural sciences and mathematics  Researcher  2009  302 
12.  10768  PhD Petar Pavešić  Natural sciences and mathematics  Researcher  2009 - 2012  242 
13.  00725  PhD Peter Petek  Natural sciences and mathematics  Researcher  2009  312 
14.  29964  PhD Vicentiu Radulescu  Natural sciences and mathematics  Researcher  2009 - 2012  488 
15.  07083  PhD Dušan Repovš  Natural sciences and mathematics  Principal Researcher  2009 - 2012  1,522 
16.  21969  PhD Jaka Smrekar  Natural sciences and mathematics  Researcher  2009 - 2012  122 
17.  13431  PhD Sašo Strle  Natural sciences and mathematics  Researcher  2009 - 2012  112 
18.  04640  PhD Marjeta Škapin Rugelj  Natural sciences and mathematics  Researcher  2009 - 2011  70 
19.  18839  PhD Aleš Vavpetič  Natural sciences and mathematics  Researcher  2009 - 2012  139 
20.  26522  PhD Žiga Virk  Natural sciences and mathematics  Researcher  2009 - 2011  131 
21.  31192  PhD Mykhaylo Zarichnyy  Natural sciences and mathematics  Researcher  2009 - 2012  79 
22.  13651  PhD Matjaž Željko  Natural sciences and mathematics  Researcher  2009 - 2012  264 
Organisations (1)
no. Code Research organisation City Registration number No. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  19,695 
Significance for science
Geometric topology and fractal geometry are two of the areas of basic research having most potential for broad affirmation in the international scientific society. Furthermore, in recent years we have successfully discovered new ways to apply our results, e.g. our work had a surprising important application in chemistry and biology in the studies of the structure of DNA. We have also discovered new applications of knot theory in magnetic field theory. We also investigate fractal geometry which has broad applications. Our results on ends of open 3-manifolds have great potential for applications in the study of the geometry of the universe. The research problems we have solved in this project have been in the center of attention by many leading experts from topology and geometry around the world for a long time. We have proposed new methods and techniques for resolving very difficult unsolved problems. Therefore our results have received a lot of interest from the international mathematical community. Our research group is well established in its area and has received many domestic and foreign awards. Our results continue to be published in leading specialized journals and that the leading members of our group continue to receive invitations to give lectures at important international conferences, confirming the international recognition of our research group. We expect to have increased interest of eminent foreign research institution in cooperation with our institute, especially from European Union. At present our research group has the largest number of international project among all Slovenian research groups in the area of mathematics. The proposed research project will also have a very positive influence for further intense development of Slovenian mathematical school, emphasizing topology and geometry and their bonds to the world research network, especially in the European Union.
Significance for the country
We have been, for several years, intensively cooperating with the industry. For example, our algorithms which we developed for generating discrete Morse functions in computational topology, can be successfully applied in radiological diagnostics, e.g. in CT, scintigraphy, internal medicine and urology. In this areas we closely cooperate with industry with some young and cutting-edge domestic hi-tech companies. Therefore we expect close collaboration also in the future. The research done in this project, will have extraordinary positive effect on the development of graduate studies in Slovenia, at every university with the PhD program in mathematics. This is especially true for education of future collaborators of our research group at the Universities of Ljubljana, Maribor, Nova Gorica and Primorska. Under the mentorship of our researchers and distinguished foreign researchers, our young researchers will prepare their PhD’s on the most up-to-date topics of modern topology and geometry. Also, we have prepared a new modern graduate course »Topology in computer science« at the Faculty of Computer Science and Informatics of the University of Ljubljana, which is of great interest also for experts in other fields, especially medicine.
Most important scientific results Annual report 2009, 2010, 2011, final report, complete report on dLib.si
Most important socioeconomically and culturally relevant results Annual report 2009, 2010, 2011, final report, complete report on dLib.si
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