National Science Centre, Poland (NCN), grant no. 2015/19/D/ST1/01184,

Principal Investigator: dr hab. Jan P. Boroński, AGH University of Science and Technology, Krakow, Poland

Researchgate website of the project with papers.

Research Project Objective: The proposed research will focus on homogeneity and minimality properties in compact spaces. The main goal will be to construct new examples of homogeneous spaces, minimal spaces and minimal systems, and investigate various related dynamical as well as topological properties. This will be in an effort to contribute to the following two well known and central questions in topology and dynamics.

1. Classify homogeneous compact spaces.

2. Classify minimal compact spaces.

Part of the effort in the project will be given to study hereditarily indecomposable continua. New examples will help build the general theory. A tangible outcome of the project will be the broadening of current state of knowledge on homogeneous, as well as minimal spaces, new publications on the subject, new discoveries of examples of such spaces, development of new methods and/or extension of the existing ones. The notions of minimality, and in particular of homogeneity not only belong to the central themes in topology and dynamics, but also relate to other areas (e.g. analysis and algebra), and in a broader sense they appear elsewhere in science, art and culture, and therefore the outcomes of the proposed research intend to reach beyond the limits determined by a narrow group of specialists.

Project Publications: (ongoing)

1. Boronski J.P.; Kupka J.; Oprocha P., Edrei's Conjecture revisited, Annales Henri Poincaré 19 (2018) 267–281

2. Boronski J.P.; Kupka J.; Oprocha P., Mixing completely scrambled system exists, Ergodic Theory and Dynamical Systems (2017) DOI:10.1017/etds.2017.16.

3. Boronski J.P.&Smith M., On the Conjecture of Wood and Projective Homogeneity, Journal of Mathematical Analysis and Applications 461 (2018) 1733–1747

4. Boronski J.P.&Clark A.&Oprocha P., A compact minimal space Y such that its square YxY is not minimal, Advances in Mathematics 335 (2018) 261-275

5. Boronski J.P.; Kupka J.; Oprocha P., All minimal Cantor systems are slow, Bulletin of the London Mathematical Society, doi:10.1112/blms.12275

6. Boronski J.P.&Clark A.&Oprocha P., New exotic minimal sets from pseudo-suspensions of Cantor systems, submitted

7. Boronski J.P.&Smith M., Continuous curves of nonmetric pseudo-arcs and semi-conjugacies to interval maps, submitted

8. Boronski J.P., G. Kozlowski On minimal manifolds, submitted

9. Boronski J.P.; Kennedy J., X. Liu, Oprocha P., Minimal noninvertible maps on the pseudocircle from the Denjoy-Rees technique, submitted

10. Boronski J.P.; Cinc J., M. Forys-Krawiec, On rigid minimal spaces, submitted

11. Boronski J.P.; Smith, M.D.; Prier D.; Sturm, F. Continuously homogeneous hereditarily indecomposable continua are tree-like, submitted