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Projects / Programmes source: ARRS

Algebra, operator theory and financial mathematics

Periods
Research activity

Code Science Field Subfield
1.01.00  Natural sciences and mathematics  Mathematics   

Code Science Field
1.01  Natural Sciences  Mathematics 
Keywords
real algebraic geometry, free analysis, group theory, Noether's problem, operators and operator semigroups on Banach spaces, positive operators, vector lattices, tropical mathematics, copulas and imprecise probability
Evaluation (rules)
source: COBISS
Points
9,710.63
A''
118.49
A'
3,080.49
A1/2
6,181.14
CI10
1,947
CImax
49
h10
20
A1
32.2
A3
1.11
Data for the last 5 years (citations for the last 10 years) on February 7, 2023; A3 for period 2016-2020
Data for ARRS tenders ( 04.04.2019 – Programme tender , archive )
Database Linked records Citations Pure citations Average pure citations
WoS  494  2,931  2,043  4.14 
Scopus  497  3,236  2,300  4.63 
Researchers (24)
no. Code Name and surname Research area Role Period No. of publications
1.  12040  PhD Janez Bernik  Mathematics  Researcher  2022 - 2023  113 
2.  28255  PhD Kristijan Cafuta  Mathematics  Researcher  2022 - 2023  29 
3.  13430  PhD Gregor Cigler  Mathematics  Researcher  2022 - 2023  56 
4.  15127  PhD Jakob Cimprič  Mathematics  Researcher  2022 - 2023  83 
5.  05478  PhD Mirko Dobovišek  Mathematics    2022 - 2023  147 
6.  16331  PhD David Dolžan  Mathematics  Researcher  2022 - 2023  125 
7.  11709  PhD Roman Drnovšek  Mathematics  Researcher  2022 - 2023  265 
8.  35334  PhD Urban Jezernik  Mathematics  Researcher  2022 - 2023  30 
9.  29584  PhD Marko Kandić  Mathematics  Researcher  2022 - 2023  61 
10.  22353  PhD Igor Klep  Mathematics  Principal Researcher  2022 - 2023  301 
11.  12190  PhD Damjana Kokol Bukovšek  Mathematics  Researcher  2022 - 2023  124 
12.  08398  PhD Tomaž Košir  Mathematics  Researcher  2022 - 2023  413 
13.  53447  Nikola Kovačević  Mathematics  Junior researcher  2022 - 2023 
14.  20037  PhD Marjeta Kramar Fijavž  Mathematics  Researcher  2022 - 2023  165 
15.  23213  PhD Blaž Mojškerc  Economics  Researcher  2022 - 2023  44 
16.  20268  PhD Primož Moravec  Mathematics  Researcher  2022 - 2023  202 
17.  22723  PhD Polona Oblak  Mathematics  Researcher  2022 - 2023  121 
18.  24328  PhD Aljoša Peperko  Mathematics  Researcher  2022 - 2023  182 
19.  32023  PhD Nik Stopar  Mathematics  Researcher  2022 - 2023  39 
20.  28585  PhD Klemen Šivic  Mathematics  Researcher  2022 - 2023  43 
21.  30826  PhD Janez Šter  Mathematics  Researcher  2022 - 2023  30 
22.  12191  PhD Aleksej Turnšek  Mathematics  Researcher  2022 - 2023  97 
23.  55096  PhD Jurij Volčič  Mathematics  Researcher  2022 - 2023  30 
24.  51877  Lara Vukšić  Mathematics  Junior researcher  2022 - 2023 
Organisations (2)
no. Code Research organisation City Registration number No. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  19,394 
2.  1554  University of Ljubljana, Faculty of Mathematics and Physics  Ljubljana  1627007  31,490 
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, the theory of operators on Banach spaces and lattices. In financial mathematics we will conduct research on stochastic analysis. In real algebraic geometry, we will investigate positive noncommutative functions and matrix convex sets. We will also explore the application of our advances to the theory of linear control systems, optimization and quantum information. In group theory, we will develop homological methods for studying the problem of Emmy Noether and its applications in algebraic geometry and K-theory. At the same time, we will also tackle modern combinatoric group theory through Babai's conjecture about the diameter of Cayley's graphs of finite simple groups. In linear algebra and algebraic geometry, we will research the classical problems of simultaneous similarity of tuples of matrices and the variety of commuting matrix tuples. We will study the properties of operators and one-parameter operator semigroups, where we will be the first to systematically go beyond Banach spaces. To this aim we will investigate other known notions of convergence and topology, especially the unbounded ones, on ordered spaces, vector lattices or Banach lattices. We will also be interested in the spectral theory of operators and related operator inequalities, where we intend to settle the 30 year old open problem of Huijmans and de Pagter. Further, we shall continue with the development of tropical methods for the studies of nonlinear operator problems. We will also strive to apply our results in financial mathematics, e.g. in the area of random processes arising from stochastic partial differential equations. With the rising importance of precise and imprecise probability in practical applications, especially in the field of statistics and finance, there is a greater than ever need for a deeper investigation and understanding of existing mathematical models for imprecise probability and for the development of new alternative models. The central role when modeling the dependence of random variables here is played by copulas. We will therefore research copulas, quasi-copulas, multivariate distributions, and the related Sklar’s theorem.
Significance for science
Achieved results will be important for the development of the mathematical sciences. Since we will be studying problems that have been raised in the international mathematical community, we expect that their solutions will attract a considerable amount of attention. The results will be very important for the development of algebra, operator theory and their applications to mathematical finance. New results will shed light on the structure of operators and families of operators. They will also be important in the study of the invariant subspace problem, real algebraic geometry, abstract group theory, and elsewhere. Many of our results have already attracted a considerable amount of attention. We expect that the same will be true going forward. We will intensively pursue and advance scientific collaboration with leading mathematicians around the world. We will publish our results in prestigious international 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 social and economic development. Our results are, we believe, 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 is directly applicable to the financial sector of the economy (insurance companies, banks, other financial institutions, etc.). We have already encountered a considerable interest from the Slovenian financial industry, the central bank, and others.
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