Supervisor: Dr Penazzi and Dr Kestner
In the recent years a strong connection between model theory and topological dynamics has been discovered, and a variety of new results have been proved by using tools from both disciplines. Topological dynamics has been developed to help describe complex dynamical systems, in which there are not only attractor points and repelling points, but also elements with recurring or quasi-recurring (orbital) behaviour. Model theory on the other hand is a systematic classification and study of all possible mathematical structures, with the aim of proving very general results which apply to a whole class of mathematical structures. Given a structure, model theory works with a special family of sets in such structure, called definable sets, and with infinite intersections of such sets, called types. When you consider a group, this group acts on its space of types, in a similar way as time acts on a dynamical system. The space of types can thus be consider as a dynamical system and the application of the group perturbates it. By repeatedly applying the group we can identify attractor points, repelling points and more importantly orbits.
Topological dynamics techniques have been used to work on a major problem in model theory, called Pillay’s conjecture, but it is believed to be of use to a wide range of problems. This is a rapidly expanding subject with a significant amount of articles recently published or submitted.
The aim of this project, in the first year (MPhil) is to study the recent articles and produce a survey paper. If deemed satisfactory, the project will then turn into a PhD studentship and the student will attack some of the key open questions. The student will have the chance to collaborate with some of the leading experts in model theory and attend seminars and conferences.
This project will be jointly supervised by Dr Penazzi (UCLan), Dr Kestner (UCLan) and Dr Tressl (Manchester)
Contact CKestner@uclan.ac.uk and DPenazzi@uclan.ac.uk if you are interested in this position.
The position is internally funded for UK/EU students. This covers fees and a bursary in line with the RCUK national stipend level (see http://www.rcuk.ac.uk/media/news/rcuk-doctoral-stipend-levels-and-indicative-fees-for-2014/ ) Funding is for 2 years for the MPhil and 3.5 years for the PhD. The deadline for applications is the 17th of April at midnight, interviews will be held at the beginning of May. The starting date is the 1st Oct 2015.