Projects / Programmes
Algebra in operator theory and financial mathematics
January 1, 2015
- December 31, 2021
| Code |
Science |
Field |
Subfield |
| 1.01.00 |
Natural sciences and mathematics |
Mathematics |
|
| Code |
Science |
Field |
| P001 |
Natural sciences and mathematics |
Mathematics |
| Code |
Science |
Field |
| 1.01 |
Natural Sciences |
Mathematics |
Noether's problem, semidefinite programming, real algebraic geometry, preserver theory, operators on Banach spaces, Stone duality, semirings, stochastic PDE
Researchers (36)
Organisations (1)
Abstract
The research program will focus on research in algebra and operator theory, and will explore their applications in financial mathematics. The main fields of research include group theory, real algebraic geometry, preserver theory and the theory of operators on Banach spaces, semiring theory and universal algebra. In financial mathematics we will conduct research on stochastic analysis.
Within group theory we will be developing new homological methods for solving Noether's problem, and their applications in algebraic geometry and K-theory will be explored. The research in real algebraic geometry will focus on finding extreme values of hermitian elements of given algebras on semialgebraic sets. Applications in control theory and optimization will be explored. We will be studying properties of operators on Banach spaces and semigroups of such operators. In addition to that, we will be describing maps preserving various prescribed algebraic properties. A part of our work will consist of developing structural theory of semirings, and exploring various generalizations of Stone duality within universal algebra. An important goal will be to find applications of our results in financial mathematics, where, in particular, we will study random processes induced by stochastic partial differential equations.
Significance for science
Achieved results will be important for the development of the mathematical sciences. Since we will be studying the problems that have been raised in the international mathematical community, we expect that they will attract a considerable amount of attention. The results will be very 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 will also be important in the study of invariant subspace problem, 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 will intensively continue with scientific collaboration with many mathematicians around the world. We will publish our results in the refereed scientific journals, present them at the international scientific meetings and at invited lectures at foreign universities.
Significance for the country
We transfer the newest scientific results to our students. In this way we contribute to the social and economic development. Our results are, by our opinion, an important part of Slovenian mathematical research, which is fundamental for many other sciences.
Research in the field of financial mathematics will contribute to the transfer of knowledge to the students of the new study program of Financial Mathematics at the University of Ljubljana. In addition, this part of our research will be directly applicable to the financial sector of economy (insurance companies, banks, other financial institutions...). We have already encounetred a considerable interest of the Slovenian financial industry, the central bank, and elsewhere.
Most important scientific results
Annual report
2015,
interim report
Most important socioeconomically and culturally relevant results
Annual report
2015,
interim report
