Projects / Programmes
Algebra, discrete mathematics, probability and game theory
January 1, 2015
- December 31, 2021
| 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 |
| Code |
Science |
Field |
| 1.01 |
Natural Sciences |
Mathematics |
algebraic graph theory, permutation groups, Schur rings, regularity, covering techniques, algorithmic graph theory, probability, mathematical biology, game theory
Researchers (42)
Organisations (3)
Abstract
The proposed research program is a continuation of the existing research program Algebra, discrete mathematics, probability and game theory (P1-0285), lead by Dragan Marušič. It includes the following organizations: the University of Primorska, the Institute of Mathematics, Physics and Mechanics, and the University of Nova Gorica.
The research program is of intra- and inter-disciplinary nature. Namely, it combines different parts of the following areas of mathematics: algebra, combinatorics with graph theory (discrete mathematics), probability, mathematical modeling and game theory with computer simulations. The program follows research goals pertaining to different fields. At the same time it creates a space for interaction of mathematicians within the Ljubljana-Koper-Nova Gorica triangle, thus contributing to the development of the university environment in the Primorska region.
Combinatorial language can often provide useful insights when studying structural properties of certain algebraic objects such as permutation groups. Conversely, when investigating structural properties of combinatorial objects admitting transitive group actions (or possibly intransitive actions with a small number of orbits), one often relies on purely algebraic results. An example of such a fruitful interplay is the main topic of the proposed program, which draws together open questions from combinatorics and algebra: groups acting on graphs, structural properties of graphs with prescribed symmetry, graph covers, blocks of imprimitivity, algebraic aspects, Schur rings and coherent configurations, etc. In addition, interactions of combinatorics and algebra with other mathematical disciplines as well as its applications in other sciences, mathematical biology, probability and game theory are studied.
The research program group has been publishing its main results in prestigious international specialized journals. Recently, the group has started to disseminate the results also in highly ranked scientific general journals such as Journal of the European Math. Society, Transactions of the American Math. Society, and Science.
In the course of the last few years the research program group hosted many leading world experts, mostly as short term visits, but some of them also for a longer period. In the future the group will try to attract even more renowned visitors as well as postdoctoral researchers, and will continue to be active in organizing international scientific meetings with distinguished participants (see http://www.famnit.upr.si/en/conferences/).
The international importance of the results obtained by the members of the group and the goals of the proposed program are well reflected in the number of publications in prestigious SCI journals and the number of pure WoS citations.
Significance for science
Apart from Art, Mathematics is 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 expected in several important areas of human activities, which will have a crucial impact in the 21st century, such as modern Economy, Safe Communications, Data protection, Decoding of Humane Genome.
The program stands at the cutting edge of today's research in all of the proposed areas. The obtained results will certainly help to better understand the subtle connections between Algebra and Combinatorics, and Graph Theory in particular. Structural results about objects, measured by the degree of their symmetry, are important in general, not only in mathematics but also in other sciences; for example in chemistry and in the 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 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 is one of the most important recent research topics, with research results frequently published in highest ranked scientific journals such as Science and Nature.
The importance of our research goals is evident from the bibliographies of the group members for the period 2009-14, from the citations of obtained results, numerous links with foreign scientists and comprehensive world bibliography in general. As with the results from the period 2009-14 we can also expect that the results obtained during the proposed program will be published in prestigious international journals and presented at international conferences. Consequently, this will give further recognition to Slovenian mathematical school in Algebra, Combinatorics, Graph Theory, Probability, Mathematical Biology and Game Theory.
Significance for the country
With the proposed program Slovenia will keep 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. But first of all the proposed program is important for Slovenia because of its aim to continue with the improvement of the good quality, world comparable School of Mathematics in UP FAMNIT which was established by this group in 2007, and already enjoy international recognition, especially with the outstanding scientific achievements.
»In the past years I successfully competed at many national and international mathematical contests. I like the fact that Famnit supports me at this and I also appreciate the opportunity to participate at the research at my age. ... The one thing I’m sure of is that mathematics will play an important role in my life.« Ratko Darda, undergraduate Math student at UP from BiH, Bronze medal on International Mathematical Olympiad 2012 (Argentina), Bronze medal on International Mathematical Olympiad 2011 (Netherlands).
»... UP FAMNIT is young and small and so I can ask quite a lot of questions at and after the classes and feel that my interest is welcome, which is important for me. ... Professors, PhD students and researchers are coming here from all over the world and not only that they teach us – we can talk to them outside the classes about mathematics, their countries or anything else. We also get to participate in math competitions, summer schools and conferences. Since I am here, studying has been a very enjoyable process for me. I feel I got in the right place. ...« Anastasiya Tanana, undergraduate Math student at UP from Belarus, 2nd Prize at International Mathematical Competition for University Students 2013 (Bulgaria), Silver medal on International Mathematical Olympiad 2012 (Argentina), Bronze medal on International Mathematical Olympiad 2011 (Netherlands).
»I come from Mexico where I studied at the National University of Mexico. I enrolled in a PhD programme on Famnit because it was a great opportunity for me to continue my studies in one of the strongest research groups in the area I’m most interested in – the Algebraic Graph Theory. ... I also want to highlight all the chances the faculty provides for participation at international conferences and vivid cooperation with research groups from all around the globe.« Sergio Hiroki Koike Quintanar, Young researcher at UP IAM and PhD student at UP FAMNIT.
»After finishing my PhD at the University of Auckland, New Zealand, I came to Koper, where I have the opportunity to work with mathematicians like prof. Dragan Marušič and prof. Aleksander Malnič, who are experts in my research area. The research group has a very good international reputation and developed strong cooperation with mathematicians from abroad. ...« Jicheng Ma, PhD, Post-doc researcher at UP IAM.
»I study symmetry in graphs and here at UP Famnit they have one of the best programmes in the world. Since they are very active in organizing conferences and workshops basically everyone from this scientific field comes to UP FAMNIT so this is where I meet the world.« Prof. Edward T. Dobson, Mississippi State University, USA and UP.
The members of the group believe that among all ways of knowledge transfer, the most important is the transmission of experience and knowledge from older generations to young. Therefore they encourage the participation of students in their projects – this way their projects get new drive and students get experience, and insight in practical use of gained knowledge.
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. With the proposed program which has a clear interdisciplinary flavor with its inclusion
Most important scientific results
Annual report
2015,
interim report
Most important socioeconomically and culturally relevant results
Annual report
2015,
interim report
