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Projects / Programmes source: ARIS

NEW METHODS IN GEOMETRY AND TOPOLOGY AND THEIR APPLICATIONS

Research activity

Code Science Field Subfield
1.01.02  Natural sciences and mathematics  Mathematics  Topology 

Code Science Field
P150  Natural sciences and mathematics  Geometry, algebraic topology 
Keywords
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
Evaluation (rules)
source: COBISS
Researchers (23)
no. Code Name and surname Research area Role Period No. of publicationsNo. of publications
1.  31193  PhD Taras Banakh  Mathematics  Researcher  2009 - 2010  322 
2.  30821  Andraž Briški-Javor  Mathematics  Junior researcher  2009 
3.  03342  PhD Matija Cencelj  Mathematics  Researcher  2007 - 2010  222 
4.  28252  PhD Dikran Dikranian  Mathematics  Researcher  2008 - 2010  205 
5.  29583  PhD Aleksandra Franc  Mathematics  Junior researcher  2008 - 2010  31 
6.  29631  PhD Boštjan Gabrovšek  Mathematics  Researcher  2009  77 
7.  25594  PhD Gregor Jerše  Mathematics  Junior researcher  2007 - 2009  27 
8.  05485  PhD Jože Malešič  Mathematics  Researcher  2007  224 
9.  14063  PhD Leila Marek Crnjac  Interdisciplinary research  Researcher  2007  93 
10.  19420  PhD Aleksandar Mijatović  Mathematics  Researcher  2007 - 2008  28 
11.  08947  PhD Nežka Mramor Kosta  Mathematics  Researcher  2007 - 2010  206 
12.  04588  PhD Dušan Pagon  Mathematics  Researcher  2007 - 2009  302 
13.  10768  PhD Petar Pavešić  Mathematics  Researcher  2007 - 2010  248 
14.  00725  PhD Peter Petek  Mathematics  Researcher  2008 - 2009  312 
15.  29964  PhD Vicentiu Radulescu  Mathematics  Researcher  2009 - 2010  488 
16.  07083  PhD Dušan Repovš  Mathematics  Head  2007 - 2010  1,537 
17.  21969  PhD Jaka Smrekar  Mathematics  Researcher  2007 - 2010  130 
18.  13431  PhD Sašo Strle  Mathematics  Researcher  2007 - 2010  116 
19.  04640  PhD Marjeta Škapin Rugelj  Mathematics  Researcher  2007 - 2010  72 
20.  18839  PhD Aleš Vavpetič  Mathematics  Researcher  2007 - 2010  146 
21.  26522  PhD Žiga Virk  Mathematics  Junior researcher  2008 - 2010  160 
22.  31192  PhD Mykhaylo Zarichnyy  Mathematics  Researcher  2009 - 2010  79 
23.  13651  PhD Matjaž Željko  Mathematics  Researcher  2007 - 2010  265 
Organisations (1)
no. Code Research organisation City Registration number No. of publicationsNo. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  20,076 
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
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