The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing either in September 2016 (funded students) or at any point in the academic year (self-funded students).
Ergodic Optimization is a novel and rapidly developing point of view within Ergodic Theory and Dynamical Systems, with close connections to Thermodynamic Formalism. It deals with those orbits of a dynamical system along which time averages (of appropriate real-valued functions) are as large as possible, or those invariant measures which maximize the space average. A hallmark of the area is the symbiosis between computer experiment and rigorous proof; consequently, it is a research .area where the inexperienced can expect to quickly make a genuine contribution.
The project will involve identifying maximizing invariant measures for various classes of dynamical system and real-valued functions, and exploring connections with certain partial orders on invariant measures induced by so-called stochastic dominance. A flavour of the area is given by the below references.
This project will be supervised by Professor Oliver Jenkinson.
The application procedure is described on the School website. For further enquiries please contact Prof Oliver Jenkinson ([email protected]
This project is eligible for several sources of full funding for the 2016/17 academic year, including support for 3.5 years’ study, additional funds for conference and research visits and funding for relevant IT needs. Applicants interested in the full funding will have to participate in a highly competitive selection process. The best candidates will be eligible to receive a prestigious Ian Macdonald Postgraduate Award of £1000, for which you will be considered alongside your application. The application deadline for full funding is January 31st 2016.
There is also 50% funding scheme available for students who are able to find the matching 50 % of the cost of their studies. Competition for these half-funded slots will be less intensive, and eligible students should mention their willingness to be considered for them in their application. The application deadline for 50 % funding is January 31st 2016.
This project can be also undertaken as a self-funded project, either through your own funds or through a body external to Queen Mary University of London. Self-funded applications are accepted year-round.
If you wish to apply, please visit the application website and mention that you wish to work on the “Ergodic Optimization and Stochastic Dominance” project.
School website: http://www.qmul.ac.uk/postgraduate/research/subjects/mathematical-sciences/index.html
V. Anagnostopoulou & 0. Jenkinson, Which beta-shifts have a largest invariant measure?
Journal of the London Mathematical Society, 79 (2009), 445--464.
O. Jenkinson, Ergodic optimization, Discrete & Continuous Dynamical Systems, 15 (2006), 197-224.