Projects / Programmes
Algebra with combinatorics and graph theory, probability and experimantal economy with the theory of expectations
January 1, 2004
- December 31, 2008
| Code |
Science |
Field |
Subfield |
| 1.01.00 |
Natural sciences and mathematics |
Mathematics |
|
| 1.07.00 |
Natural sciences and mathematics |
Computer intensive methods and applications |
|
| Code |
Science |
Field |
| P110 |
Natural sciences and mathematics |
Mathematical logic, set theory, combinatories |
permutation group, transitivity, primitivity,
group character, semiregular element, elusive group, bilinear form, K-theoretic invariant,, ordered-coherent ring , distance regularity, strongly regular graph, association scheme, antipodalcover,automorphism lift,regular map, highly transitive graph, configuration, design, criptography, finite field,
eliptic curve, Delannoy numbers, stochastic processes, cellular automata,statistical physics, financial and actuarian mathematics,mathematical statistics, game theory, experimental economy,theory of expectations.
Researchers (25)
Organisations (3)
Abstract
This research program is a happy marriage of three areas of mathematics: algebra, combinatorics with graph theory and probability. Moreover, via mathematical modelling and computer simulation, experimental economy and the study of social systems are also touched upon.
Significance for science
Mathematics is apart from Art the only universal language of human communication present in all developed civilizations. It is a basis of Natural Sciences and lies in the heart of theoretical Computer Science. Abstract mathematical theories are used in Physics, Engineering, Computer Science and also in Social, Economic and Biomedical sciences. Therefore the influence of Mathematics may be be expected in several important areas of human activities, such as, modern Economy, Safe Communications, Data protection, Decoding of Humane Genome – which will make a criucial mark to the 21st century. The program standed at the cutting edge of today's research in all of the areas dealt with by the members of the group. The obtained results are helpful for a better understanding of subtle connections between Algebra and Combinatorics, and Graph Theory in particular. Structural results about objects, measured with the degree of their symmetry, are important in general, not only in mathematics but also in other sciences; for example in chemistry and theory of elementary particles. Also our work on probability extends well beyond a strictly mathematical framework with significant consequences in other sciences. Let as only mention Genetics as one of the most propulsive fields of research today. The multidisciplinary aspect of the program gives additional value to this program, with problems, solutions and results being reflected in hot areas of research such as, experimental economy and the theory of expectations. In particular, the problem of human cooperation which is one of the most important recent research topics, with research results frequently published in highest ranked scientific journals such as Nature. The importance of our research goals can be seen from program group members’ bibliography, the citations of obtained results, numerous links with foreign scientist and comprehensive world bibliography in general. The results obtained during the program were regularly presented at international conferences and they are published in prestigious international journals. Consequently, this gave a further recognition to Slovene mathematical school in Algebra, Combinatorics, Graph Theory, Probability and Game Theory.
Significance for the country
With the program Slovenia is keeping in touch with modern trends in mathematics. Moreover, with inclusion of Game Theory it goes hand in hand with contemporary methods of mathematical modeling based on computer simulations and laboratory verifications (There is a lack of knowledge, teaching, and applications of Game Theory in Slovenia, on the academic level as well as in everyday life - where it is especially applicable.). But first of all the program is important for Slovenia because it creates the basis for an excellent quality School of Mathematics in the newly established UP FAMNIT. These stormy times of social changes call for an even tighter incorporation of Mathematics into scientific research and education thus enabling a faster technological development in Slovenia. Our group already has many experiences in this field. In particular the program had a clear interdisciplinary flavor with inclusion of many strong elements of Applied Mathematics. Let us conclude with the following statements. Our existence as a fully developed nation in Europe depends as much on preserving our language and culture as it depends on having a highly educated population. It is thus necessary to be able to use different communication channels – and mathematics, as a universal language, is a key factor here. Hence, the above discussion shows that the program played an essential role in the strengthening of Slovene national identity, in particular in its western, most vulnerable part of Primorska.
Most important scientific results
Final report,
complete report on dLib.si
Most important socioeconomically and culturally relevant results
Final report,
complete report on dLib.si
