Research topics

  • Mathematical economics: Efficiency models and visualization in production theory and financial portfolio theory
  • Econometrics and statistics: Linear regression models, analysis of regularly varying functions, theory of extreme values, statistical analyses in economics and social sciences
  • Differential geometry: Theory of submanifolds, curvature conditions on translation surfaces, visualization of curves and surfaces
  • Computer vision: Invariance, 3D image analysis and reconstruction, image and video metrology
  • Physics: Thermal and thermo-acoustic waves

E.g., current projects are

  • Theoretical analysis of univariate and multivariate regularly varying functions and sub exponential functions. These analyses are motivated by probability theory and have applications in extreme values theory, renewal theory, ruin probabilities, central limit theorems and generalizations.
  • Fundamental research in extreme values statistics leading to ways of estimating high quantiles or small probabilities among others. Examples can be found in finance (e.g., value at risk) and insurance (e.g., probability of large claims that could threaten solvability).
  • Theoretical research and application of efficiency models in production theory and financial portfolio theory. The models developed require linear or nonlinear optimization methods and can be used on a wide range of practical cases when efficiency measuring is required.
  • Development of scientific and educational visualizations in production theory and financial portfolio theory.
  • Realization of statistical analyses (e.g., general linear regression models), mainly in economics and social sciences.
  • Mathematical and statistical support of ongoing research in economics.
  • Fundamental research in differential geometry, especially in the theory of submanifolds. Several curvature conditions are studied on translation surfaces (e.g., the Weingarten condition that requires a functional relation between distinct types of curvature).
  • Fundamental research in computer vision with applications in forensic image and video metrology and self-calibrating 3d-reconstruction.
  • Fundamental research on the use of thermal and thermo-acoustic waves for nondestructive examination of material layers.
  • Development of scientific and educational visualizations of curves and surfaces and their geometrical properties.
  • Development of specialized software useful in ongoing research.