Instantons on manifolds of exceptional holonomy

PGR-P-606

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Key facts

Type of research degree: PhD
Application deadline: Ongoing deadline
Country eligibility: UK and EU
Funding: Competition funded
Source of funding: University of Leeds
Supervisors: Dr Derek Harland
Schools: School of Mathematics
Research groups/institutes: Pure Mathematics

<h2 class="heading hide-accessible">Summary</h2>

Instantons are connections on vector bundles over Riemannian manifolds that minimise a natural functional (the Yang-Mills functional). They were first studied by theoretical physicists in the context of gauge theories that form part of the standard model, but soon attracted the interest of differential geometers, leading to spectacular insights into four-manifold topology, amongst other developments.<br /> <br /> The goal of this project is to study instantons on manifolds with exceptional holonomy -- more precisely, Riemannian manifolds of dimension seven or eight with holonomy contained in G2 or Spin(7). This area of research is motivated by efforts to extend successful work with four-manifolds, and by problems arising in string theory and other areas of mathematical physics. Possible directions include constructing examples (using techniques from analysis, group theory or elsewhere) and studying the moduli spaces of instantons.

<h2 class="heading">How to apply</h2>

<p>Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University's website</a>. Please state clearly in the Planned Course of Study section that you are applying for <em><strong>PHD Pure Mathematics FT</strong></em> and in the research information section that the research degree you wish to be considered for is <em><strong>Instantons on Manifolds of Exceptional Holonomy</strong></em> as well as <a href="https://eps.leeds.ac.uk/maths/staff/4034/dr-derek-harland">Derek Harland</a> as your proposed supervisor.</p> <p>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</p> <p> </p>

<h2 class="heading heading--sm">Entry requirements</h2>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

<h2 class="heading heading--sm">English language requirements</h2>

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.

<h2 class="heading">Funding on offer</h2>

<p><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>UK </strong>– The <a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a>, <a href="https://phd.leeds.ac.uk/funding/198-akroyd-and-brown-scholarship-2022">Akroyd & Brown</a>, <a href="https://phd.leeds.ac.uk/funding/199-frank-parkinson-scholarship-2022">Frank Parkinson</a> and <a href="https://phd.leeds.ac.uk/funding/204-boothman-reynolds-and-smithells-scholarship-2022">Boothman, Reynolds & Smithells</a> Scholarships are available to UK applicants.  <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p><strong>Non-UK </strong>– The <a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a> is available to nationals of China. The <a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens.  <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p>

<h2 class="heading">Contact details</h2>

<p>For further information regarding your application, please contact Doctoral College Admissions by email: <a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a>, or by telephone: +44 (0)113 343 5057.</p> <p>For further information regarding the project, please contact Dr Derek Harland: <a href="mailto:d.g.harland@leeds.ac.uk">d.g.harland@leeds.ac.uk</a>.</p>

<h3 class="heading heading--sm">Linked research areas</h3>