Projects / Programmes
NEW METHODS IN GEOMETRY AND TOPOLOGY AND THEIR APPLICATIONS
| Code |
Science |
Field |
Subfield |
| 1.01.02 |
Natural sciences and mathematics |
Mathematics |
Topology |
| Code |
Science |
Field |
| P150 |
Natural sciences and mathematics |
Geometry, algebraic topology |
asymptotic topology, atomic decomposition, Bing-Whitehead compactum, coarse geometry, chaos, Conway polynomial, cohomological dimension, compact metric space, Floer homology, fractal geometry, geometric group theory, Hausdorff dimension, Higson corona, homotopy self-equivalence, knot, link invariant, Lorenz attractor, nilpotent group, Novikov conjecture, Peano continuum, quantuum group, quaternion, rigid embedding, Seiberg-Witten theory, Seifert genus, spectrum, stable homotopy, wild Cantor set, 3-manifold, 4-manifold, Hilbert cube
Researchers (23)
Organisations (1)
Abstract
A three year project of fundamental research in mathematics is proposed, its main aim being the investigation of important unsolved problems in the following fields of geometry, topology and their applications: asymptotic dimension theory, cohomological dimension theory, coarse geometry, Higson coronas, Peano continua, wild fractals in Euclidean spaces, homotopy theory, Seiberg-Witten invariants in dimension 4 and computational topology. We shall study connections between the theory of knots and links and the magnetic field theory. We shall also investigate properties of the E-infinity Cantorian space-time. Publication of our results in mathematical journals and monographs is planned. Dissemination of the results will be via participation at conferences, seminars, and workshops, as well as through colloquia at foreign universities and institutes. A new monograph, first on this topics, dedicated to homology manifolds, will be written. The proposed project is related to our current bilateral projects with United States, Japan, France, Spain, Russia. This project will also have a significant impact on the preparation of doctoral students in geometry and topology.
Significance for science
The project had a very positive impact on the development of postgraduate education in this field of mathematics in Slovenia. Under the supervision of our researchers and visiting scientists our doctoral students worked on their theses. With the active participation of our members at the international conferences and the visits from abroad we continued the very successful development of topology and geometry in Slovenia and our international collaboration expanded even farther. Within the framework of our international projects we organized numerous visits by leading experts to Slovenia.
We consider topology as one of the areas of the fundamental research which have the greatest potential for a wide affirmation in the international scientific community. Our project group is well established in our field and it has won several prizes. The proposed research problems have been for a long time in the focus of several leading experts in topology and geometry, in particular from the United States, Japan, the European Union and Russian Federation. Therefore the expected results in these fields are of great interest to the international mathematical community.
Our results continue to be published in leading international mathematical journals. We shall publish a special monograph on cell-like mappings and homology manifolds with the European Mathematical Society. We continue to receive invitations for plenary talks at important specialized international conferences, confirming the international status of our group. We also recorded an increase in the interest by foreign research institutions for a collaboration - at present our project group has the greatest number of international projects in the field of mathematics in Slovenia.
Significance for the country
The successful work of our research program team will have an important impact on the quality of the undergraduate and (especially) graduate education v Sloveniji in the field of topology and geometry. In particular, our team has introduced a new modern graduate course "Topology in Computer Science" at the Faculty of Computer Science of the University of Ljubljana, which is very interesting also for experts in other fields, in particular from medicine. The algorithms developed for generating discrete Morse functions in computational topology can be successfully applied to the studies in radiological diagnostics, eg. for CT and scintigraphy in gastroenterology and urology. We also published a new university textbook on topology.
Most important scientific results
Annual report
2008,
2009,
final report,
complete report on dLib.si
Most important socioeconomically and culturally relevant results
Annual report
2008,
2009,
final report,
complete report on dLib.si
