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PhD Student Applications

PhD Applications

The postgraduate research degree offered at the School of Mathematics is the PhD.  The PhD programme is three years in length with an additional year to write up and submit your thesis should it be needed. However, please note if you are offered a fully funded place, you will receive four years of funding (stipend and all fees). The students admitted typically have an MSc degree, or 1 st  class honours degree (or its international equivalent). From the start of their studies, they are assigned a main supervisor with whom they work closely throughout their degree programme and a second supervisor who provides additional help and pastoral support. Applications are invited for PhD studies for September each year. Occasionally students are admitted at other times of the year by special arrangement.  To request the possibility of admission at another time of the year, please  email  the Graduate School with further details of your request. 

All applications received by  22 January 2024 will receive full consideration for funding.  Later applications will be considered until all positions are filled.

If you are applying for EDCS or the China Scholarship, please ensure you check the relevant application deadline. These scholarships do require a separate application.  The deadline for EDCS applications is 19 February 2024.

We accept applications from students who have secured external funding at all times of the year - Please make this clear on your application, and if you are in contact with a potential supervisor.

How to Apply

Step 1: meet our entry requirements.

Our minimum entry requirements are a 1 st  class Honours degree (or its international equivalent) OR a 2:1 Honours degree (or its international equivalent) plus a Masters degree (or its international equivalent) in a relevant subject. Typically, candidates have a good understanding of the field they propose to study, and some research experience.

Students applying for a research degree should identify their research interests and determine in which  research group  they wish to carry out their work. They are encouraged to contact staff members prior to their application in order to identify possible research projects and supervisors. However, it is not essential for you to have secured a supervisor before submitting your application. You can note proposed supervisor(s) on your appliction form.

Non-UK candidates may be required to provide a evidence of proficiency in the English language. For full details on English language requirements, please see this page . Applicants must have one of the following qualifications as evidence of their English language ability:

an undergraduate or masters degree, that was taught and assessed in English in a majority English speaking country as defined by UK Visas and Immigration ( UKVI list of majority English speaking countries ) 

• IELTS Academic: total 6.5 with at least 6.0 in each component
• TOEFL-iBT : total 92 with at least 20 in each section
• PTE(A) : total 61 with at least 56 in each of the Communicative Skills scores
• CAE and CPE : total 176 with at least 169 in each paper
• Trinity ISE : ISE II with distinctions in all four components

Degrees taught and assessed in English must be no more than 3.5 years old at the date of the beginning of your degree programme. English language test certificates must be no more than 2 years old at the beginning of your degree programme, or 3.5 years for CAE & CPE.

Step 2: Apply online

Make an online application to the appropriate PhD programme(s) (see below) . You will be asked to upload documents at the start of the application process. 

The documentation that we require you to upload to your application is:

• Interim or final transcript(s)  - (depending on what stage you are at in your studies) of your Undergraduate Degree, and Masters Degree, if applicable.
• Final degree certificate(s) - for your Undergraduate Degree, and Masters Degree, if applicable.
• Two academic references to be provided directly by referees. Enter their names and email addresses in the required areas, and an automated email will be forwarded to them requesting a reference upload. We will not accept references uploaded by applicants.
• A CV - You can upload this in the place of a research proposal, which is not required for your application.
• English Language Test Certificate (where applicable) - please see here . 

Where you are asked for your project proposal, you may ignore that request, the School of Mathematics does not require a research proposal . Although the EUCLID application system will request that you upload one, you can just ignore this request. The reason that you will be asked for one is that the system applies to all Schools throughout the University and some Schools do require a research proposal. In the place of a research proposal, please upload an up to date CV. There is no need to upload any certificates for the degree you are currently studying (if you have not been issued one) - instead, official interim transcripts will be required.

Official translations of any documents not in written English are required. 

On the application form, where it asks for funding information - please enter 'School of Mathematics'. Each application will automatically be considered for one of our scholarships. Please indicate any other potential source of funding you have, have applied for or are intending to apply for (see Step 3).  If you have secured external funding, please provide evidence of the funding along with your application.

Step 3: Funding

Please review and apply for all applicable sources of funding noted on the What funding is available for your PhD  page.

Please apply via the research pages below:

• Algebra PhD
• Analysis PhD
• Applied and Computational Mathematics PhD
• Geometry and Topology PhD
• Mathematical Physics PhD
• Optimization and Operational Research PhD
• Probability & Stochastic Analysis PhD
• Statistics PhD
• Mathematics Education

• Schools & departments

What is the Doctoral College?

The University of Edinburgh Doctoral College is a coordinating structure for all postgraduate researchers, supervisors and relevant staff at the university, designed to enhance and support the postgraduate student experience. 

For information and resources for research staff, please see the Research Staff Pages:  https://www.ed.ac.uk/researchers

The Doctoral College are holding two welcome events for new Postgraduate Researchers at the University of Edinburgh. These welcome events will give you the opportunity to hear from the Doctoral College leads and representatives from across the University about how the Doctoral College can help you to make the most of your time at Edinburgh.

On Campus Welcome - Tuesday 10th September at 10am. Find out more here  

Online Welcome - Tuesday 1st October at 1pm. Find out more here

PhD stories

Our extraordinary PhD students come from all walks of life and all backgrounds. In this collection of short videos, some of them share their experiences -  PhD Stories

Vision and strategy

The purpose of the Doctoral College, our vision, strategic objectives and our commitment to the improvement of postgraduate research cultures

People and structure

About the Doctoral College leadership and management structure, and the wider Doctoral College team.

Personal and professional development and training

Information about professional, careers and personal development training and opportunities for  UoE   PGR  students.

Researcher Representation and Community

Information on student representation and community

Support for PGR supervision

Information and guidance for staff who supervise research students.

Doctoral training centres

Information on funded PhD training programmes and support for directors and administrators of these programmes.

Essential information for postgraduate researchers

Code of Practice for Supervisors and Research Students (PDF)

College of Arts, Humanities and Social Sciences - PGR pages

College of Medicine and Veterinary Medicine - PGR pages

College of Science and Engineering  (EASE log in required)

Information for prospective postgraduate research students

New student pages

Postgraduate study degree finder

This article was published on 2023-12-07

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Study Engineering at the University of Edinburgh

Engineers are at the forefront of innovation. We contribute to the transition to a lower carbon future; next generation materials and processes; devices for medical diagnosis; data-driven innovation, energy, robotics and AI systems; and make infrastructure and the environment safer and healthier. It’s an exciting, hands on subject that inspires you to challenge the way things are done, to think creatively and develop solutions that could genuinely make a difference to the world.

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Available PhD projects

Explore available PhD projects in the physical sciences or social sciences

Physical sciences PhD projects

Find available PhD projects in the physical sciences.

Social sciences PhD projects

Find available PhD projects in the social sciences.

This article was published on 2024-07-01

Schools & departments

PhD Study with Edinburgh Neuroscience

Edinburgh Neuroscience currently has about 250 PhD students working on a wide variety of neuroscience-related projects that cover health and disease across the life course, from early development to old age. Our PhD students are an integral part of our dynamic neuroscience community and we are keen to recruit motivated and collaborative students.  There are a variety of PhD opportunities, advertised throughout the year and, in addition to the numerous individual PhD projects offered via our research centres, we have two PhD programmes.

EdNeuro.PhD is our PhD portal

To find out more about studying for a PhD with Edinburgh Neuroscience, currently available funded studentships and how to apply, please visit our dedicated PhD portal  EdNeuro.PhD

Visit EdNeuro.PhD for all our PhD training information

Our PhD Programmes

SPRINT-MND/MS PhD Programme . Led by Edinburgh Neuroscience, Scottish PhD Research & Innovation Network Traineeships in MND/MS’ is a PhD programme in partnership with the Universities of Aberdeen, Dundee, Glasgow and St Andrews and promotes research into all aspects of motor neurone disease and multiple sclerosis.

Wellcome Trust 4 year PhD in translational Neuroscience . Our flagship PhD programme  ‘Translational Neuroscience: Lifecourse influences on human brain health’ is a ‘ training to translate ’ programme for non -clinical students that addresses a current global need by focussing on the advancement of knowledge, expertise and skills in clinical translation, drawing on unique Edinburgh research strengths in diseases across the life-course to achieve this goal.

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PhD by Distance

All PhD programmes at ECA have the PhD by Distance option, with full-time or part-time study.   

The programmes are: 

• PhD in Architecture   
• PhD in Architecture by Design    
• PhD in Architectural History    
• PhD in Art    
• PhD in Creative Music Practice    
• PhD in Cultural Studies    
• PhD in Design    
• PhD in History of Art    
• PhD in Landscape Architecture    
• PhD in Music    
• PhD in Musical Composition   

How you will study

The PhD by Distance mode is available to all applicants for eligible ECA PhD programmes, who will apply via the Postgraduate Degree Finder. Applicants will select between on-campus and distance options, as well as between part-time and full-time options. 

Students enrolled on the PhD by Distance mode will not be expected to come to Edinburgh to study but visits for particular activities (tutorials, annual reviews, research training courses, workshops, etc) can be considered on a case-by-case basis and within UKVI visa regulations. 

• View UKVI visa regulations   

It is however expected that PhD by Distance students will come to Edinburgh for their oral (viva voce) examination, although options for online vivas may be considered on a case-by-case basis. For practice-based students, how practical work will be shared with supervisors will be explored in detail at the point of application by both subject area PGR Director and potential supervisor(s); in-person presentation of work (such as a musical performance) may occasionally be necessary. Access to studios and workshops for PhD by Distance students will be limited, as these require to be prioritised for on-campus students. 

PhD by Distance students will receive the same level of support and supervision as on-campus students but with supervisory sessions taking place via Teams, Zoom, or another video conferencing platform, rather than on-campus and in-person. The frequency with which students will meet with their supervisors will be provisionally agreed at the point of application and confirmed during induction. Supervisors (and examiners) will not make site visits to PhD by Distance students.  

There are no mandatory courses for ECA PhD students. A range of generic and specific research methods and skills training courses are available online from university.  

PhD by Distance students will have access to all University of Edinburgh support services and will be able to access online library resources/support and home use software through University site licenses in the same way that all students can. 

Please be aware that some scholarships and funding are not open to PhD by Distance applicants, for example AHRC regulations currently state that students must live within a reasonable distance from their University so are only eligible for applicants to on-campus PhD programmes.

How to apply and entry requirements

If you'd like to study on a postgraduate research programme at Edinburgh College of Art, you must apply through EUCLID, our online application system. You can find out how to do this on the University of Edinburgh website, where you'll also be able to: 

• see detailed entrance requirements for each programme on the Degree Finder  
• get information on what to expect after you apply  
• find out about study modes, start dates and fees  
• find out if, and how, you need to submit a portfolio, showreel or research proposal  
• find out where to go for further advice and guidance 

Application process

Before you apply  .

Students are assigned two research supervisors, the second of which may be from another discipline within ECA, or from somewhere else within the College of Arts, Humanities & Social Sciences (CAHSS) or wider University. 

Please ensure that at least one member of staff (see below) maintains an active research programme that aligns with the themes of your proposed project.  

Prospective students are strongly encouraged to make contact with the relevant member(s) of staff via email to explain your research interests prior to submitting an application. Please note that we only accept applications and review application materials submitted through the official EUCLID application portal.

After you apply 

Once your application has been submitted for consideration, it will be sent to a team of academic reviewers for their attention. They will then make a decision about your application and research topic, and decide whether it is possible to make an offer of a place to study with us. You may be asked to attend a brief online interview but if this is the case, you will be notified in advance. 

Apply through the Postgraduate Degree Finder on the University of Edinburgh website

Complete the distance learning application form (Word document download)

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• Schools & departments

Edinburgh Doctoral College Scholarships (EDCS)

The University of Edinburgh offers PhD scholarships for students starting their PhD research in the academic session 2024/25.

The School of Informatics will award one Edinburgh Doctoral College Scholarship (EDCS) for the current academic session. 

The scheme is highly competitive and applicants must be of outstanding academic merit and research potential. Candidates are selected and ranked at School level, based on the strength and quality of their PhD application, research proposal, references and scholarship application.

Candidates wishing to be considered for this scholarship need to submit a separate scholarship application, via the Scholarships Portal, which is located in EUCLID and can be accessed via the MyEd portal.

The deadline for EDCS applications for entry in the academic sessions 2024/5 is 8 February 2024.

For more information, please check the links below:

Edinburgh Doctoral College Scholarships - UK Students

Edinburgh Doctoral College Scholarships - International Students

This article was published on 2024-03-18

The Precourt Institute for Energy is part of the Stanford Doerr School of Sustainability .

Stanford Energy Postdoctoral Fellowship program introduces nine new fellows

The energy-centered postdoctoral research program is nurturing a global community of future leaders to realize sustainable, affordable, secure energy for the world.

Stanford University welcomes nine energy-focused postdoctoral scholars as the second cohort of its Stanford Energy Postdoctoral Fellowship . The program is run by the Precourt Institute for Energy , with support from Stanford’s TomKat Center for Sustainable Energy , Bits & Watts Initiative , and StorageX Initiative , and from several philanthropists.

The recent PhD graduates arrive from nine different universities and from six  home countries over three continents. Five of the incoming energy fellows are women, and four are men. Between the first two cohorts of Stanford Energy fellows, 83% of the 17 fellows are international, and 41% identify as non-male.

The objects of the newest cohort’s sustainable energy research at Stanford are also diverse, ranging from technological solutions to adapting to climate change. Their mentors are in 16 different academic departments. In addition to faculty members, scientists at SLAC National Accelerator Laboratory and at Carnegie Institution for Science's two departments at Stanford – Plant Science and Global Ecology – also mentor these early-career scholars.

“This fellowship is designed to identify, cultivate, and connect the next generation of pioneers in search of sustainable energy for all people,” said Yi Cui , the program’s founder and faculty director. “Each of these postdocs are working on projects that may lead us in promising new directions in technology, research, analysis, and policy.”

Successful candidates emerge through a demanding, competitive process. Each potential fellow must be nominated by at least two Stanford researchers from different disciplines to be their co-mentors, among other requirements. The program’s faculty advisory board , led by Nobel laureate and former U.S. secretary of energy, Steven Chu , selects the successful candidates following a rigorous interview process. 

“Congratulations to each of our new fellows. We’re excited to welcome you to campus and to the Stanford energy ecosystem,” said William Chueh , faculty director of the Precourt Institute. “As you get to know each other, members of the first cohort, and our fellows’ Stanford mentors, we hope that the multidisciplinary nature of our program will provide you with new insights on how to solve the energy challenges you take on.”

The fellowship covers full living and professional costs for three years, one year longer than most postdoctoral programs. This extra year affords fellows the opportunity to mine a new research vein that diverges from their PhD work.

Aspiring scholars interested in forming next year’s cohort of energy postdoctoral fellowships are encouraged to apply now . The deadline for applications is Oct. 1. Third cohort fellows will begin their term between July 1 and Sept. 1, 2025.

Building a community

The new postdocs will research various energy-related topics. These include biofuels, hydrogen production, climate adaptation, new battery designs, a modern electricity grid, energy-efficient AI, and airborne methane, which is one of the more egregious of the greenhouse gases.

“These fellows come with a broad range of expertise in fields stretching from advanced microscopy and engineering to data science and economics. In common, though, they now pursue solutions for the global energy transition through interdisciplinary research,” said Audrey Yau , the fellowship’s director. “We look forward to seeing how their work grows through faculty mentorship, engagement with their peers, and exposure to novel, interdisciplinary ways of thinking.”

The fellows join a broad sustainability-minded scientific community at the Stanford Doerr School of Sustainability, of which the Precourt Institute and its many programs are a significant segment. This sense of community is critical to the fellows’ success, Yau said. The fellowship hosts monthly “lab crawls” where fellows visit other fellows’ research spaces to learn about their studies, as well as regular leadership lunches where fellows learn from the lived experiences of leaders in their field. The program also organizes social activities for fellows and their mentors, and it offers a professional development program as a springboard to what comes after the fellowships are complete. 

“This second cohort, just as the first, can put their stamp on this fellowship, which we expect to contribute significantly to the clean energy transition around the world for decades,” said Yau. “The 2025 cohort will also help define this program’s culture of collaboration and early history of high-impact research.”

Meet the 2024 fellows

Liat Adler is in the very challenging pursuit of biofuels from algae. Some algae can use the energy from light to produce hydrocarbon oils. A barrier to harvesting that sustainable fuel: the production of oil is limited by energy delivery from photosynthesis and is too low to be economically viable. Adler’s energy fellowship will look to boost algae productivity by tweaking how they convert light into chemical energy, potentially doubling oil output. Adler completed her PhD studying algal photosynthesis at the University of Edinburgh in Scotland. Adler is advised by Matthias Garten in Stanford’s Departments of Microbiology and of Bioengineering, as well as Adrien Burlacot and Arthur Grossman , both of Carnegie’s Department of Plant Biology.

Every time you scroll through your phone or browse the internet on your computer, there is a high chance that there is an artificial intelligence (AI) behind what you see on the screen—and it's using a lot of energy. Fabia F. Athena studies emerging materials and devices that aim to lead us toward low-power AI hardware. Athena’s research will explore fabricating emerging semiconductor devices at low temperatures for energy-efficient computer logic and memory, supporting low-power AI systems. That would align this great technological progress with sustainability. Athena earned her PhD in electrical and computer engineering at Georgia Tech studying energy-efficient emerging materials for brain-inspired computing. Athena is advised by H.-S. Philip Wong in electrical engineering, and Alberto Salleo in materials science and engineering.

Cong Chen studies how distributed energy resources – like rooftop solar, electric vehicles, home batteries, heat pumps, and HVAC systems – can be aggregated to support an electric grid increasingly reliant on intermittent supplies, like wind and solar power. In her fellowship, Chen’s focus will be threefold: equitable and efficient energy dispatch and pricing, understanding energy customers' preference, and improving power grid resilience. She recently earned her Ph.D. in electrical engineering at Cornell University studying power system engineering, optimization theory, and power system economics. Chen is advised by Kuang Xu and Omer Karaduman at the Graduate School of Business and Itai Ashlagi in management science and engineering.

Elemental sulfur, usually considered an industrial byproduct, could speed the shift from liquid to solid-state batteries while driving down costs. But there are technical challenges standing in the way. Yukio Cho will center on the molecule-by-molecule construction of atomic-scale interfaces inside these solid-state batteries to prevent degradation and boost redox kinetics. A material chemist, Cho has a special interest in nanomaterials and electrochemical applications. During his doctoral studies at MIT, Cho used a similar self-assembly platform to create a novel nanomaterial with remarkable stability and robustness for use in recyclable batteries and one-dimensional nanocatalysts. Cho will be advised by Stacey Bent in chemical engineering and Jagjit Nanda at SLAC.

Xinyu Dou studies methane emissions monitoring. She earned her PhD at Tsinghua University exploring how global greenhouse gas emissions are evolving in response to the energy transition and their correlated climatic implications. While at Tsinghua, Dou helped develop the world’s first nearly real-time, grid-level carbon emissions database. Her overarching goal is to improve such systems. By using satellite monitoring of key communities and through machine learning that can generate insights from vast emissions datasets, such monitoring could guide policy decisions and technological advances. Dou is advised by faculty members Rob Jackson in Earth systems science and Adam Brandt in energy science and engineering.

Kieran Orr will research highly conductive solid electrolytes to replace the harmful and flammable liquid electrolytes currently used in batteries. The precise ion transport mechanisms in solid electrolytes are poorly understood, so, in his fellowship, Orr will employ SLAC’s X-ray diffraction capabilities to develop atomic-scale, real-time structural probes to understand exactly how ions move through solid electrolytes. Previously, at the University of Cambridge, Orr used techniques to understand how strain affects halide perovskite materials used in solar energy, lighting, and detector technologies. Orr will be advised by Aaron Lindenber g in materials science and engineering and in photon science at SLAC, William Chueh in materials science and engineering, energy science and engineering, and photon science, and David Reis in applied physics and photon science.

Lisa Rennels works at the intersection of economics and computer science, researching the economic impacts of climate change, climate policy, and decision-making under uncertainty. She focuses on integrated assessment modeling and how bringing a rigorous treatment of uncertainty and risk to these models informs, and complicates, economic analysis for policy. In her fellowship, Rennels will focus on impacts to human health and building software for climate change research. She earned her PhD in Energy and Resources at UC-Berkeley. At Stanford, Rennels will be advised by Inês Azevedo in energy science and engineering and Marshall Burke in environmental social sciences. 

Microscopes have long been essential tools for exploring material at small scales, driving significant advancements in energy technologies. However, optical microscopy technologies capable of observing down to the single-ion level are yet to be developed. Yecun Wu ’s fellowship aims to address this gap by employing quantum sensors to optically capture and visualize the behaviors of individual ions, providing deeper insights into the complex physics and chemistry of batteries and other sustainable energy systems. Wu earned his Ph.D. in electrical engineering at Stanford in 2023, where he studied two-dimensional materials for use in quantum and energy applications. Wu will be advised by Stephen Chu in physics and in energy science and engineering, and Yi Cui in materials science and engineering, energy science and engineering, and photon science.

Zisheng Zhang did his doctoral work at UCLA in theoretical and computational chemistry where he advanced models for dynamic restructuring catalyst surfaces. Catalysis is key in energy conversion and storage, and for other environmental and green chemistry applications. Developing high-performance electrocatalysts that do not use noble metals is especially desirable for sustainability and scalability. Zhang thinks that boride, a compound of Earth-abundant boron and various metals, could be an exceptional electrocatalyst. He has dedicated his fellowship to developing and applying computational models to understand and design mixed boride electrocatalysts for applications in hydrogen evolution, nitrogen reduction, and other important reactions. Zhang will be advised by Thomas Jaramillo in chemical engineering, energy science and engineering, and photon science, and Frank Abild-Pedersen at SLAC.

Cui is also faculty director of the Sustainability Accelerator at the Stanford Doerr School of Sustainability , co-director of the Precourt Institute's StorageX Initiative, past director of the Precourt Institute for Energy, and senior fellow at the Precourt Institute and the Stanford Woods Institute for the Environment . Chu is also professor of molecular and cellular physiology at Stanford School of Medicine . Bent is also Stanford's vice provost for graduate education and postdoctoral affairs. Jackson is a senior fellow at the Precourt and Woods institutes. Brandt is also director of the Precourt Institute's Natural Gas Initiative . Reis is also director of the Stanford PULSE Institute . Azevedo is co-director of Precourt's Bits & Watts Initiative. Burke is also a senior fellow at the Freeman Spogli Institute , at the Woods Institute, and at the Stanford Institute for Economic Policy Research (SIEPR). Jaramillo is also director of the SUNCAT Center for Interface Science & Catalysis , where Abild-Peterson is the co-director.

The Precourt Institute is part of the Stanford Doerr School of Sustainability.

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• Schools & departments

Online programmes

Search the degree finder, browse degrees by type.

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• A-Z of online programmes

Browse degrees by school

About our degrees.

We offer a range of options for postgraduate study: from professional qualifications to independent research, on-campus taught programmes to part-time, online study. Find out which graduate study option is right for you:

• Studying with us

PhD in Financial Technology

Building on our established PhD in Management programme, we have developed an innovative new doctoral programme in the field of Financial Technology.

PhD in Financial Technology allows students to pursue their own research topic in the area of Financial Technology or apply for specific industry projects, where students will be able to address complex industrial challenges to gain real-world experience.

This programme aims to prepare students for a diverse array of careers in finance. Approximately 50% of students who pursue the industry pathway, can expect to build on the networking opportunities available to them from studying at the international partners' premises during their study and move into a permanent career in that company, or the industry after graduation.

PhD in Financial Technology at a glance

• Study over three years full-time or six years part-time, with an additional 'writing-up' year available to all.
• Develop advanced techniques and in-depth knowledge in the field of Financial Technology.
• Study an independent research topic or participate in fully funded opportunities working with leading industry partners.
• For those on the industry pathway, study both at the University of Edinburgh campus and at an industrial partner's location, with guidance from academic colleagues and industry specialists at all times.
• We encourage our students to aim higher, presenting papers at prestigious conferences and submitting articles for publication.
• Access to a wide range of professional and personal development opportunities during your studies.
• While we invite students from around the globe to join our community, we don't offer this programme online or by distance learning.

Entry requirements

Find out our academic, English language, and application requirements for the PhD in Financial Technology.

Programme overview

View the learning outcomes and a typical training course schedule for a first-year student.

Fees and living expenses

When budgeting please consider associated administration fees and expenses as well as our funding support.

Ready to apply?

Review our application checklist and make your application to the PhD in Financial Technology.

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