Algebra in operator theory and financial mathematics

The results of the research group are important for the development of the mathematical sciences. Since we study problems that were raised in the international mathematical community, we expect they will attract a considerable amount of attention. The results are important for the development of algebra and its application to the operator theory. New results will shed light on the structure of certain families of operators. They are also important in the study of invariant subspace problem, study of commuting matrices, symmetries of graphs, real algebraic geometry, abstract theory of groups and semigroups and elswhere. Many of our results have already attracted a considerable amount of attention. We expect that the same will be the case also for our future results. We successfully continued with scientific collaboration with many mathematicians around the world. We have published our results in the refereed scientific journals, presented them at the international scientific meetings and at invited lectures at foreign universities.

The members of the research group are also university lecturers. This enables us to acquaint our students with the most recent scientific development, either achieved within our group itself or by other researchers, and thus contribute to the socio-economical development of Slovenia. Our achievements constitute an important part of the Slovene mathematical science, which is fundamental for other sciences. Our efforts in developing the scientific foundations of financial mathematics will have considerable impact on financial institutions.