Date added: 2023-01-18
Groups of Manifold Transformations: dynamical and probabilistic point of view
Professor Tomasz Szarek will be conducting research tasks of the project in cooperation with scientific units from Chile, France, the Netherlands and Israel. In addition, a scholarship holder and a post-doc will be employed in order to perform the research project with the assist of the Principal Investigator. The duration of the project will be 48 months.
The research team will deal with the dynamic and probabilistic aspects in the theory of mapping groups. These aspects will imply two different classes of issues. The first will be devoted to ergodicity of minimal operations and distortions in groups of homeomorphisms of a manifold. In the second, the emphasis will be placed on random maps, i.e. maps selected randomly from a certain group or at least a semi-group of transformations. Moreover, the research team plan to deal with limit theorems for Markov chains corresponding to random transformations. In particular, a central limit theorem, law of the iterated logarithm and large deviation principle are expected to be established.
The National Science Centre, for the implementation of the research project, led by prof. Tomasz Szarek, PhD. Eng., granted financing in the amount of PLN 413 112.
Congratulations and best wishes of further success!