(PN) MATHEMATICS, APPLIED

The research activities of the Applied Mathematics Group of the UPN focus on the development of mathematical models, methods and algorithms and simulation procedures to solve complex problems in the financial-economic sector and support the growth of both traditional financial institutions, such as banks and insurance companies, and innovative companies. Research topics include, but are not limited to:

Fields of research:

• Statistics for Stochastic Processes in Continuous Time 
• Time Series Analysis
• Econometrics
• Nonparametric Statistics

- Numerical linear algebra (accurate and fast matrix algorithms, solving eigenvalue and singular value problems, perturbation theory, eigenvalue and singular value problems for matrices with elements from noncommutative fields)

Series and summability in normed spaces
Topological modules
Composition Operators
Lipschitz Spaces
Bishop-Phelps-Bollobás Property
Measure Theory in effect algebras
History of Mathematical Analysis

Group transformations:symmetries and equivalence transformations.
Conservation laws.
Nonclassical method. Potential symmetries.
Mathematical modelling of chemotherapy resistance in tumor development.
Exact solutions,Quañitative analysis.
Nonlinear waves and solitons.
Nonlocal symmetries and nonlocal related systems.
Diffusion systems: bacterial growth, tumor evolution. Other models from physics, medicine, engineering and economy.

The research is focused on realizations of noncommutative spaces in the context of deformation theory and their applications to geometry and physics. Specifically, we investigate realizations of the kappa-deformed space, the Lorentz and Poincare algebras as well as general Lie-algebra type noncommutative spaces by formal power series in the Heisenberg-Weyl algebras and their generalizations. We also study realizations of some Lie superalgebras which arise naturally in the geometry of differential forms on noncommutative spaces.