Research interests of employees reflects the structure of the Faculty. Since the Statute of AGHUST forces relatively large departments, division of departments in addition to "groups" were introduced. At the departments and the groups operate socalled "research groups" focusing people working on close issues.
Department of Mathematical Analysis, Computational Mathematics and Probabilistic Methods is divided into two groups: Group of Mathematical Analysis and Group of Computational Mathematics and Probabilistic Methods.
Within the Group of Mathematical Analysis there are two research groups:

research group "Functional Analysis"
research group "Functional Analysis"
,
Employees of the research group deal primarily with the general spectral theory of operators and its applications. In particular, these are issues such as: lifting of comutant of selected classes unlimited operators, immersion of a Hilbert and Krein space, creation and annihilation operators for an infinite number of variables in the Fock and Bargmann spaces, spectral analysis of Schrodinger, Dirac, Pauli, Jacobi operators, perturbed operators of WienerHopf type etc.
Results concern the structure of spectrum of operators. Results were also obtained for the
asymptotic spectral theory, eigenvectors and eigenvalues of unlimited Jacobi operators were examined.
New projectioniterative methods for a class of operator equations (in particular for difference equations) were constructed and variational methods for selected nonlinear boundary problems were also developed.

research group "Approximation and Theory of Operators"
research group "Approximation and Theory of Operators"
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Employees in this group deal primarily with the spectral theory of operators, frames, the theory of splines and wavelets, properties of the minimum projection and dynamic systems.
The obtained results concern the unlimited matrix representations of operators of the frames, property of Gabor frames, property of the minimum projection, Chebyshev splines and their applications.
The scientific activity of the Group of Computational Mathematics and Probabilistic Methods concentrates on the following two areas:

computational mathematics
computational mathematics,
This includes such topics as:
1. complexity of the continuous problems in a variety of computational models
2. linear methods for ordinary differential equations
3. complexity of stochastic integration and stochastic differential equations
4. quantum algorithms for nonlinear tasks
5. resistant stability of polynomials and pseudopolynomials
6. computer aided research in mathematical physics
7. Conley index

mathematical statistics
mathematical statistics.
This includes such topics as:
1. inverse problems for Poisson processes
2. asymptotic approximations for optimal compatibility tests
3. use of regression models with shape constraints to detect change points
4. resampling method for point processes
Employees of the Group also deal with the application of mathematics in other sciences, in particular, use of numerical methods for solving complex engineering problems and applications of statistical methods in biological and medical sciences. Within the Group of Computational Mathematics and Probabilistic Methods, research group "Computational Complexity of Continuouity" works.
Scientific activities of employees of the Department of Discrete Mathematics applies to discrete mathematics with particular emphasis on:
theory of graphs, combinatorics and theoretical computer science
theory of graphs, combinatorics and theoretical computer science.
Subjects works from the theory of graphs, combinatorics and theoretical computer science
 Packing of graphs, digraphs and hipergraphs
 Distributions of graphs, digraphs and hipergraphs (divisions cyclic graphs and complete hipergraphs, themselves complementary graphs and hipergraphs)
 Arbitrary distributions
 Cycles and paths in graphs (in particular, Hamiltonian issues)
 Extreme issues (graphs and hipergraphs saturated due to the path, (H,k) stable minimumsized graphs)
 Divisions (line divisions cubic graphs, geometric divisions)
 Coloring and labeling of graphs (among others edge coloring differentiating vertices)
 Topological aspects (the theory of knots)
 Theoretical computer science
Within the Department of Discrete Mathematics, there are two research groups: research group "Combinatorial Analysis" and research group "Theory of Graphs" with a nonempty intersection of areas of interest.
The scientific activity of employees of the Department of Financial Mathematics is manifested mainly in the works of:
research group "Stochastic Control in Finance"
research group "Stochastic Control in Finance"
.
Members of the research group deal with include:
 the application of stochastic control to optimize the investment in the bond market
 study the optimization of dividends
 construction of a realistic structural model of credit risk
Within the Department of Differential Equations, there are two research groups:
 research group "Differential Geometry" that studies issues of
differential geometry
differential geometry
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Interest of the research group include a number of issues of differential geometry, global analysis and topology. In particular the following topics:
 Properties of algebraic groups of automorphisms of geometric structures;
 The theorems of reconstruction in differential geometry;
 Lie theory for infinite dimensional Lie groups;
 Basic properties of groups of homeomorphisms
 The application of the above issues.

research group "Differential Equations and Dynamical Systems", which deals with analytical, qualitative and numerical studies of
differential equations and dynamical systems
differential equations and dynamical systems
.
Main subjects of research of the research group:
1. The use of measure theory, topological methods and computerassisted proofs for the study of discrete and continuous dynamical systems. In particular, the issue of chaos in discrete systems, normally hyperbolic manifold in the continuous systems, theory and application of Conley index.
2. The study of systems of nonlinear differentialfunctional equations of parabolic and elliptic type. In particular, the study of existence and uniqueness of the solutions in the case of infinite systems of equations of mentioned types, the study of convergence and stability of the differece methods for such systems.
3. Application of methods based on the theory of Lie groups (whose use is particularly useful in models of the natural sciences), qualitative and functional methods for constructing and testing solutions to nonlinear equations of mathematical physics and biology (in particular, the solutions describing localized wave structures and their impact). In particular, a study of convectionreactiondiffusion equations and their hyperbolic modification, nonlocal continuous models, searching for physical succinct solutions, testing their stability and attraction properties.
More details on the scientific interests of employees of the Faculty provides publication list of employees (which included works published since 2001) and seminars held at the Faculty, and conferences, the Faculty has organized or coorganized.