Research Areas

The research in the Institute of Computer Science has been driven by two sources: the intrisic beauty of mathematics as well as the necessity to solve practical problems in fields as diverse as applied computer science and foundations of computer science. Naturally, this encourages an interdisciplinary approach in our educational programs.

The faculty have achieved national and international recognition for their research, and many have also had extensive experience doing applied mathematical and computer science research at the most prestigious scientific research institutions in Poland and outside.

The areas of active faculty research include Foundations of Computer Science, Applied Computer Science, and Applied and Computational Mathematics.

Foundations of Computer Science:

  • Algorithmic Analysis
  • Automated Theorem Proving
  • Combinatorial Optimization
  • Combinatorial Semigroup Theory
  • Computational Complexity
  • Cryptography
  • Finite Model Theory
  • Graph Theory
  • Lambda Calculus
  • Logic Programming
  • Petri Nets
  • Theory of Automata and Formal Languages
  • Theory of Codes
  • Theory of Computation

Applied Computer Science:

  • Artificial Intelligence
  • CAD/CAM Integration
  • Computer Graphics
  • Diagnostic Expert Systems
  • Diagrammatic Reasoning
  • Feature-based Design
  • Geometric Modeling and Reasoning
  • Graph Transformations
  • Neural Networks
  • Syntactic Pattern Recognition
  • Theory and Applications of Pattern Recognition
  • Theory of Graph Grammars and their Parsing
  • Theory of Distributed Parallel Algorithms

Applied and Computational Mathematics:

  • Markov Operators
  • Mathematical Theory of Optimal Control
  • Mathemathical Modeling in Engineering, Biology, Medicine and Economy
  • Measure Theory
  • Numerical Analysis
  • Ordinary and Partial Differential Equations and their Applications
  • Philosophy of Mathematics
  • Probability Theory
  • Stochastic Differential Equations
  • Topological and Computational Dynamics

Subjects of current research are following:

* Chair of Applied Computer Science:
syntactic pattern recognition, CAD/CAM integration, diagnostic expert systems, neural networks, theory of graph grammars and their parsing.

* Chair of Computational Mathematics:
boundary value problems, qualitative theory of ordinary differential equations, algorithms for computing homology, Conley index theory for discrete multivalued dynamical systems.

* Chair of Optimization and Control Theory:
optimal shape design for systems described by partial differential equations, variational inequlaities and hemivariational inequalities.

* Division of Discrete Mathematics:
symbolic dynamics, theory of codes, retracts of free semigroup.

* Division of Probability Theory:
stochastic differential equations, applications of statistics in economy, applications of probability theory in measurements, existence of invariant measures of Markov transformations.