Understanding Extremal Processes in Dynamical Systems - Mathematics - EPSRC DTP funded PhD Studentship Ref: 2896

About the award

This project is one of a number funded by the Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership to commence in September 2018. This project is in direct competition with others for funding; the projects which receive the best applicants will be awarded the funding.

The studentships will provide funding for a stipend which is currently £14,553 per annum for 2017-2018. It will provide research costs and UK/EU tuition fees at Research Council UK rates for 42 months (3.5 years) for full-time students, pro rata for part-time students.

Please note that of the total number of projects within the competition, up to 15 studentships will be filled.

Dr Mark Holland

Streatham Campus, Exeter

Project Description

This PhD studentship project aims to understand extremal processes for chaotic dynamical systems. The scope lies at the interface of mathematical analysis and probability.

A challenging and active area in dynamical systems is that of return time statistics. Namely, given a dynamical system and a specific region of phase space, what is the probability distribution that governs the times of first return to this region? The proposed project will exploit recent developments on the theory of return time statistics to determine (weak) convergence to an extremal process for dynamical systems. Such processes arise naturally within extreme value theory, and can be used to determine the probabilistic properties of the time series of maxima, as generated by the dynamical system. In the case of suitably normalised Birkhoff sums the natural limit process arising is that of a Brownian motion. Thus this project aims to understand the corresponding limit processes for normalised maxima of the time series.

For time series generated by independent identically distributed random variables, weak convergence to an extremal process is known to occur. However, for time series generated by a dynamical system new ideas are needed to establish convergence. This project will develop a theory to determine when weak convergence to an extremal process occurs for a general dynamical system, and apply the theory to particular examples such as discrete time hyperbolic dynamical systems, and continuous time chaotic systems governed by ordinary differential equations. 

This project will use approaches in mathematical analysis of dynamical systems, and will be of benefit to those seeking to work in pure or applied mathematics, or to those working within statistical modelling of extremes for weather/climate. Given good progress, the project will explore extremes in low dimensional weather models (e.g. Lorenz equations).

Entry Requirements
You should have or expect to achieve at least a 2:1 Honours degree, or equivalent, in Mathematics. Experience in probability, dynamical systems is desirable.

The majority of the studentships are available for applicants who are ordinarily resident in the UK and are classed as UK/EU for tuition fee purposes.  If you have not resided in the UK for at least 3 years prior to the start of the studentship, you are not eligible for a maintenance allowance so you would need an alternative source of funding for living costs. To be eligible for fees-only funding you must be ordinarily resident in a member state of the EU.  For information on EPSRC residency criteria click here.

Applicants who are classed as International for tuition fee purposes are NOT eligible for funding. International students interested in studying at the University of Exeter should search our funding database for alternative options.


Application deadline:10th January 2018
Value:3.5 year studentship: UK/EU tuition fees and an annual maintenance allowance at current Research Council rate. Current rate of £14,553 per year.
Duration of award:per year
Contact: Doctoral Collegepgrenquiries@exeter.ac.uk

How to apply

You will be required to upload the following documents:
•       CV
•       Letter of application outlining your academic interests, prior research experience and reasons for wishing to
        undertake the project.
•       Transcript(s) giving full details of subjects studied and grades/marks obtained.  This should be an interim
        transcript if you are still studying.
•       If you are not a national of a majority English-speaking country you will need to submit evidence of your current
        proficiency in English.  For further details of the University’s English language requirements please see

The closing date for applications is midnight (GMT) on Wednesday 10 January 2018.  Interviews will be held at the University of Exeter in late February 2018.

If you have any general enquiries about the application process please email: pgrenquiries@exeter.ac.uk.
Project-specific queries should be directed to the supervisor.

During the application process, the University may need to make certain disclosures of your personal data to third parties to be able to administer your application, carry out interviews and select candidates.  These are not limited to, but may include disclosures to:

• the selection panel and/or management board or equivalent of the relevant programme, which is likely to include staff from one or more other HEIs;
• administrative staff at one or more other HEIs participating in the relevant programme.

Such disclosures will always be kept to the minimum amount of personal data required for the specific purpose. Your sensitive personal data (relating to disability and race/ethnicity) will not be disclosed without your explicit consent.