Mathematics consists in proving the most obvious thing in the least obvious way.
George PolyaAkcije dokumenta
P1-0285 - Algebra, discrete mathematics, probability and game theory
Head of program P1-0285: prof. dr. Dragan Marušič
Duration: 01/01/2022 - 12/31/2027
Abstract: The research program is a natural follow up of the research program P1-0285 2015-2021. It is of intra- and inter-disciplinary nature. Interactions of combinatorics and algebra with other mathematical disciplines as well as applications in other sciences, mathematical biology, probability and game theory are studied. Reseach content and goals of this research program are divided into six fields: (1) Algebra with Combinatorics and Graph Theory, (2) Other Algebraic Tools for Studying Graph Properties, (3) Hereditary Graph Classes, (4) Mathematical Studies of the Evolutionary Dynamics, (5) Probability, (6) Game Theory. 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 program (covering (1) - (3)), 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, even/odd automorphisms, intersection densities, Schur rings, Terwilliger algebras, preservers, etc. The Classification of finite simple groups (CFSG), while having proved to be a powerful tool in this kind of research, may sometimes obscure the structural content of the problems dealt with. Consequently, searching for direct CFSG-free proofs, whenever possible, will also be a focus of P1-0285. The proposed program also aims at making UP FAMNIT (the establishment of which has been an important achievement of P1-0285) a Center of Excellence in mathematics, modeled after some existing centers in certain countries comparable to Slovenia. As a consequence of ensuing strengthening of mathematical research at the University of Primorska and the two partner institutions (University of Nova Gorica and Institute of Mathematics, Physics and Mechanics), a spillover effect is expected in Slovenian science and beyond.