Fundamentals of Computing and Discrete Mathematics

FiDiPro Group

Project leaders: Juhani Karhumäki and Luca Zamboni


This group is supported by a 5 year research grant from the Academy of Finland through the Finnish Distinguished Professor Programme (FiDiPro). The research undertaken is an interdisciplinary study of various topics on the complexity and combinatorics of infinite words on a finite set of symbols which model complex dynamical systems arising in mathematics, physics and computer science. In most cases the approach undertaken exploits the rich interaction between the combinatorics and complexity of infinite words, and the underlying arithmetic/diophantine properties of the system(s) in question. The topics include:

  1. Problems related to the general theory of complexity of infinite words in one and more dimensions;
  2. general problems arising in study of formal languages in connection with complexity, periodicity, recurrence, codes, and automaticity.
  3. theoretical and computational aspects of automata theory;
  4. symbolic, ergodic, and diophantine properties of geometric dynamical systems including substitution generated systems in one or more dimensions, tilings, Bratteli diagrams and Markov odometers, Toeplitz flows, and cellular automata;
  5. self-assembly and modeling of biological phenomena.

We will be running a regular Distinguished Lecture Series in which the most respected names in the field would be invited to Turku to deliver a colloquium talk and to teach a one to two week long doctoral level topics course. These courses would target the needs and interests of our current students and would be open to all students participating in the Consortium.

A main objective of our group is to create an International Consortium in the general area of Combinatorics on Words centered at FUNDIM. It would involve the participation of various research centres in mathematics, computer science, theoretical physics, and biology from around the world. The primary objective of the Consortium is to pursue and enhance scientific research at the highest international level with a strong emphasis on Ph.D education and postdoctoral training. It would facilitate exchanges between the participating institutions and provide greater synergy. It would also allow some excellent yet scientifically isolated research centres to integrate through collaboration with the greater international scientific community. We hope to establish formal conventions between the various doctoral programs participating in the Consortium to facilitate exchange and co-mentoring of doctoral students, and allow joint doctoral degrees with special emphasis on interdisciplinary research dissertations.

Recent Updates

February 2013:
Last modified: