Projects / Programmes
Nestandardne vložitve Cantorjeve množice v Evklidski 3-prostor (Slovene)
| Code |
Science |
Field |
Subfield |
| 1.01.02 |
Natural sciences and mathematics |
Mathematics |
Topology |
| Code |
Science |
Field |
| 1.01 |
Natural Sciences |
Mathematics |
Researchers (22)
Organisations (1)
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
