Research Areas

Fundamentals and Applications of Computer Science:

The Institute of Computer Science of Jagiellonian University carries out research on the basics of computer science, applications of computer science, as well as applied and computational mathematics. Such research topics lead to the inclusion of interdisciplinary applications in our educational programs. The institute's research staff is known in Poland and abroad for their high-quality research. They have experience conducting research in the field of computer science and mathematics. Research is currently being conducted on the following topics:

Fundamentals and Applications of Computer Science:

  • Genetic and evolutionary algorithms
  • Algorithm analysis
  • Automatic theorem proving
  • Diagnostic expert systems
  • Symbolic dynamics
  • Computer Graphics
  • Combinatorics on words
  • Combinatorial theory of semigroups
  • Cryptology
  • Combinatorial Optimization
  • Programming
  • Real-time systems
  • Computer Networks
  • Neural networks
  • Syntactic recognition of images
  • Agent systems
  • Artificial intelligence
  • Automata, formal languages, and grammars theory
  • Graph theory
  • Theory and applications of image recognition
  • Code theory including block codes
  • Theory of distributed parallel algorithms
  • Calculation theory
  • Machine learning
  • Computational complexity

Applied mathematics, computational and applications of mathematics:

  • Numerical analysis
  • Topological dynamics
  • Computational topology
  • Mathematical modeling in engineering, mechanics, biology, medicine, and economics
  • Mathematical theory of optimal control
  • Markov operators
  • Theory of probability
  • Differential and partial equations and their applications
  • Stochastic differential equations
  • Measure theory

Both national and international research projects are carried out. The results of this research are presented at national and international scientific conferences and are significant in many fields of computer science.

The research conducted at the Institute is mainly financed by research grants from the Ministry of Science and Higher Education, European grants, as well as smaller grants obtained from other sources. Scientific conferences organized by us were co-financed, for example, by domestic and international companies. The development and modernization of the teaching base of the Institute are carried out mainly with the use of funds from the Jagiellonian University and investment grants from the Ministry of Science and Higher Education.

A large part of the scientific and research work at the Institute of Computer Science is carried out in international cooperation with, among others, centers in Austria, France, Greece, Japan, Canada, Korea, Germany, Switzerland, the USA, Great Britain, and Italy, as well as in cooperation with research centers in the country.

The scientific activity of the Institute of Computer Science of Jagiellonian University is conducted in extensive cooperation with computer scientists and mathematicians from other research centers and in international cooperation with many scientific and research institutions around the world.

In addition to joint work and the exchange of scientific information, good contacts with these and many other scientific institutions around the world allow us to refer our best Ph.D. students for post-doctoral research internships.

Key scientific achievements:

  • Development of a method of computer-supported proofs of the existence of chaotic invariant sets in dynamical systems and carrying out such proof for the famous system of Lorenz equations. This achievement required the development of completely new numerical and combinatorial algorithms in the field of dynamical systems and topology, proof of their correctness, and their implementation for practical applications. The publication co-authored by prof. dr hab. M. Mrozek on this issue was recognized by the "Encyclopedia Britannica" as one of the four most important achievements in mathematics in 1995.
  • Obtaining by the team of prof. dr hab. Z. Denkowski's existential results for hemivarious inequalities of the parabolic and hyperbolic type and the application of the Gamma, G and PG-convergence theory to the analysis of sensitivity and numerical stability of optimal solutions in optimal control tasks for systems described by ordinary and partial differential equations, differential inclusions, variational and hemivariative inequalities.
  • The results obtained by the team led by dr hab. W. Forys in the field of combinatorial theory of semigroups, combinatorics on words, theory of formal languages, and algebraic coding theory. Study of algorithmic, lattice and topological properties of retracts, providing characteristics of asymptotic properties of words that are iterates of free monoids homomorphisms; developing the basis of the theory of "block" codes, constructing algorithms for generating a variety of languages ​​using the technique of fixed points and characterizing the family of countably recursive languages.
  • The best research workers at the Faculty of Mathematics and Computer Science of Jagiellonian University in 2005-2008 were dr hab. Leszek Gasiński, prof. dr hab. Stanisław Migórski and dr Anna Ochal from the Department of Optimization and Control of the Institute of Computer Science.