Research Associate (FTC - 42 months)

Job Description

FTE and working pattern: 35 hours per week (1 FTE), Fixed term contract for 42 months

The Post description:

Applications are invited for a Postdoctoral Research Assistant (PDRA) position, funded through the EPSRC standard grant “On Multiscale Methods”, led by Prof. Michela Ottobre. The post will be held at the Department of Mathematics of Heriot Watt university and at the Maxwell Institute, Edinburgh, and will be for a fixed term of up to 42 months (3 and a half years). The successful applicant is expected to start on May 1^st , 2025 (with some flexibility, upon pre-agreement). 

The project leader is happy to be contacted for informal discussions and to provide more information on the project – email at m.ottobre@hw.ac.uk 

What you would be doing: 

You will carry out and disseminate research in applied stochastic analysis and related fields (write and submit academic articles). You will work on aspects of the proposed project together with the project leader and her collaborators (more detail on the project below), and take the lead on agreed aspects of the project. You will contribute to the supervision of PhD students.

You will actively engage with the thriving research community in applied mathematics of Heriot Watt University and the Maxwell Institute – through participation/organization of seminars/reading groups, knowledge exchange activities, as appropriate - and will be offered the opportunity to further your professional and personal development skills.

The project leader will support the successful applicant in their academic, scientific and professional growth. 

What we are looking for:

• Background and track record of research in one or more of the following fields: stochastic analysis, analysis, probability, statistical mechanics. 

More specifically, background in one or more of the following topics is highly desirable: interacting particle systems, mean field theory, McKean-Vlasov stochastic differential equations, multiscale methods for stochastic differential equations and/or for partial differential equations, Markov semigroup theory, diffusion and/or jump processes, calculus of variations, PDE theory. The detailed description of the project (below) will provide more context. 

• A keen interest in developing theory which is motivated by applications
• Some level of fluency with standard programming languages such as Matlab or Python. 
• Excellent oral and written communication skills
• The successful applicant will show initiative and independence, in order to manage and achieve project deliverables and deadlines; and will participate in, and develop, networks and collaborations within the Maxwell Institute, nationally and world-wide

About the group, Heriot Watt and the Maxwell Institute:

The PDRA will work closely with the project leader and with her group and network of collaborators. Parts of this project will be in collaboration with B.Goddard (University of Edinburgh), Iain Souttar (Warwick University) and Konstantinos Spiliopoulos (Boston University), among others. More broadly, the PDRA will join the Applied and Computational Mathematics and the Analysis and Probability groups at Heriot Watt and the Maxwell Institute.

HW is an internationally-leading research institution, whose dynamic research environment is complemented by the partnership with University of Edinburgh. Such a partnership has led to the creation of a common research hub, the Maxwell Institute (MI) for Mathematical Sciences, www.maxwell.ac.uk, a recognised centre of excellence which ranked 3^rd in the UK for quality and breadth of its research at REF2021. The MI has an established research record across the spectrum of Mathematical Sciences and coordinates a wide spectrum of activities, including a large graduate school (which comprises two centres for doctoral training), numerous seminar series, Knowledge Exchange and outreach events and distinguished lecture series. 

HW has also a central role in the running of the International Centre for Mathematical Sciences (ICMS) www.icms.org.uk, a world-renowned conference centre, and one of the three research infrastructures in the UK (the other two being in Cambridge and Warwick). The ICMS further enriches the research environment and research culture of the MI, by attracting a constant flow of national and international research visitors. 

The PDRA will benefit from exposure to this stimulating research community and from interactions with the large number of world-class mathematicians who regularly visit HW, ICMS and the Maxwell Institute.

Detailed description of project:

The project is in applied stochastic analysis, more specifically it is concerned with the development of multiscale methods for stochastic dynamics which are multiscale in time. The dynamics considered in this project are (mostly) either stochastic differential equations or continuous time random walks. The core issue that this project will address is the development of a theory which enables to treat slow-fast systems, when the fast system has multiple invariant measures (equilibria). 

The analysis of systems which are multiscale in time is commonly dealt with thorough the use of (stochastic) averaging and homogenization techniques. When using these methods a key assumption is that the dynamics for the fast scale is ergodic, i.e. that it admits a unique invariant measure (more precisely, one assumes that the so called `frozen process’ is ergodic, for each fixed value of the slow process). Under this assumption, the purpose of multiscale methods is to derive a reduced dynamics, which well approximates (in some appropriate sense) the initial fast-slow system. 

The goal of this project is to bring conceptual and analytical advances to the field of multiscale methods, by producing a coherent framework to tackle the study of systems which are multiscale in time, when the fast process has multiple invariant measures. While this project is primarily devoted to developments in stochastic analysis, its goals are application driven and so it is important that the applicant would be willing to gain a “broader perspective” on the matter. 

Stochastic processes with multiple invariant measures naturally arise in the study of interacting particle systems and associated mean field limits. Such systems are paradigmatic models in statistical mechanics and kinetic theory, in connection with the study of collective navigation and consensus formation. While statistical sampling has been one of the main motivations for the development of ergodic theory, many processes in natural and engineered systems are likely to exhibit multiple invariant measures. This includes the tendency of fireflies to synchronise their flashing or not, the microstructure of nematic crystals aligning to several distinct equilibrium configurations (giving rise to different material properties), the opinion formation process in social media, which can converge towards various possible outcomes. 

The non-ergodicity of the fast process creates interesting mathematical structures, and new types of ansatz are needed to describe the limiting reduced dynamics. Moreover, when the system is multiscale both in time and in space, it is important to understand the interplay between the two scales. And, to complete the picture, it is relevant for applications to understand how well the reduced dynamics approximates the original fast-slow system – for example whether the reduced dynamics is a good approximation on finite or infinite time intervals. 

Further Information:

This 42 month (3 and a half years) position has no teaching load, but comes with the possibility of taking on some light teaching duties, should the candidate wish to gain teaching experience. 

The position also includes:

• A training budget will be made available to sustain the overall growth of the PDRA e.g. to attend leadership programmes, public engagement courses as well getting support from our additional programmes offered by Heriot Watt University
• The applicants selected for interview will be invited to be interviewed in person, where possible (reasonable travel costs will be supported where possible).
• Heriot Watt University has a relocation policy to help individuals who will join the institution from a different location www.hw.ac.uk/uk/services/docs/hr/policies/UK_Relocation_Policy_and_Procedure.pdf
• This particular grant does allow for the National Health Service surcharge and a significant contribution to the visa fees to be included in the relocation package should that be applicable.

Essential Criteria:

• Applicants should hold (or be about to obtain) a PhD in mathematics or neighbouring discipline and have an excellent track record of work in at least one of the following research fields: probability, analysis, stochastic analysis, statistical mechanics. 
• Evidence of a developing publication record
• Evidence of excellent oral and written communication skills
• Ability to work independently and as part of a group

How to Apply:

Applications with full CV and a research statement can be submitted up to midnight (UK time) on Friday, 31st January 2025.  The CV can be either in standard or in narrative format https://www.ukri.org/what-we-do/supporting-healthy-research-and-innovation-culture/research-and-innovation-culture/supporting-the-community-adoption-of-r4r-like-narrative-cvs/narrative-cvs-what-they-are-and-why-use-them/. The research statement should be no longer than two pages of A4 and contain a brief overview of the research interests of the candidate.   

The interviews are anticipated to be conducted in February 2025.

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