Scientific activity of the members of the MACMPM department concentrates on the following topics:

• approximation and theory of operators: spectral theory of operators, frames, theory of splines and wavelets, properties of minimal projection and dynamic systems. The obtained results concern matrix representations of operators of the frames, properties of Gabor frames, properties of minimal projection, Chebyshev splines and their applications;

• computational mathematics: information-based complexity for continuous problems, general linear methods for ordinary differential equations, complexity of stochastic integration and stochastic differential equations, quantum algorithms for nonlinear problems, robust stability of fractional systems, computer assisted methods in mathematical physics, applications of numerical methods in complex engineering problems;

• functional analysis: general spectral theory of operators and its applications, lifting of comutant of selected classes of unbounded operators, embedding 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 Wiener-Hopf type etc. Results concern the structure of spectrum of operators. Results were also obtained for the asymptotic spectral theory, eigenvectors and eigenvalues of unbounded Jacobi operators were studied. New projection-iterative 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;

• mathematical statistics: inverse problems for Poisson processes, asymptotic approximations for optimal goodness-of-fit tests, change point problems in regression models with shape constraints, resampling methods for point processes and periodic processes, applications of statistical methods in biology and medical sciences, confidence bands in nonparametric curve estimation.

Members of the MACMPM department publish in journals such as: Applied Mathematics and Computation, Integral Equations and Operator Theory, ISA Transactions, Journal of Complexity, Journal of Computational and Applied Mathematics, Journal of Mathematical Analysis and Applications, Journal of Multivariate Analysis, Journal of Operator Theory, Journal of Scientific Computing, Journal of Statistical Planning and Inference, Linear Algebra and Its Applications, Quantum Information Processing, Statistica Sinica, Test, Topological Methods in Nonlinear Analysis and many others.