The Institute carries out research work in the following areas:

  • Theory of normed spaces, quasi-normed and F-normed spaces, including geometry of function spaces.
  • Interpolation of linear operators. 
  • Operators on spaces of analytic functions. 
  • Toeplitz and Hankel operators. 
  • Applications of differential geometry and symmetry theory (Galois symmetries) in problems of mathematical physics. 
  • Differential and algebraic geometry, Hodge structures. 
  • Variational calculus.  
  • Hyperelliptic integrals and special functions. 
  • Deformation of autonomous systems with ordinary and magnetic separable potentials to non-autonomous Frobenius integrable systems.
  • Approximation theory in function spaces. 
  • Qualitative theory of difference equations (asymptotic properties of solutions, their oscillability, boundedness, stability).  
  • Classes of difference equations (equations of neutral type, equations with quasi-differences, Volterra equations, rational equations) and their applications e.g. in modelling in economics, biology and technology). 
  • Asymptotic properties of s-numbers for general diagonal operators. 
  • Reliability engineering of land transport modes.  
  • Statistical analyses regarding: 
    • analysis of the degree and type of tree damage in various stands (e.g. pine stands) during thinning after harvester work (e.g. Komatsu 931.1 harvester), 
    • soil research, the impact of various organic fertilization on quantitative changes in various nutrient ratios in cultivated plants, toxicity testing (heavy metals). Multivariate statistical models with structured covariance. 
      Optimality of experimental designs under the models with interference effects. 
  • Experimental and computational studies of pendula dynamics. 
  • Analysis of inverse problems of nonlinear mechanics. 
  • Application of asymptotic methods to study the problems of nonlinear mechanics. 
  • Studies of the properties of Köthe spaces over non-Archimedean fields and continuous linear operators between these spaces. 
  • Mathematical and numerical modeling of thin-walled and multilayer structures. 
  • Modeling mass and heat transfer problems given by non-linear differential and integral equations.
  • Optimization algorithms for heat and mass transfer inverse problems.