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Geometry and Dynamics of Topological Solitons

PGR-P-595

Key facts

Type of research degree
PhD
Application deadline
Ongoing deadline
Project start date
Tuesday 1 October 2024
Country eligibility
International (open to all nationalities, including the UK)
Funding
Competition funded
Source of funding
University of Leeds
Supervisors
Dr Derek Harland and Professor Martin Speight
Schools
School of Mathematics
Research groups/institutes
Pure Mathematics
<h2 class="heading hide-accessible">Summary</h2>

Field theory is the natural mathematical language to explain fundamental physics, from particle physics, to condensed matter, to gravitation and cosmology. In many field theories it is possible for the dynamical field, a map from spacetime into some manifold, to wrap itself up rather like a high-dimensional knot. Such a field traps large amounts of energy in a smooth, spatially localized lump, called a topological soliton, which can move around and interact with other solitons in remarkably particle-like fashion. Solitons are natural candidates for fundamental particles (e.g. magnetic monopoles, protons, neutrons), but they also model large scale structures in condensed matter physics (e.g. vortices in superconductors) and cosmology (e.g. cosmic strings). There is a beautiful geometric theory of the dynamics of solitons which describes their motion in terms of the moduli space of static multisolitons, a mathematically rich and fascinating object in its own right. The aim of this project is to study the geometry of topological solitons and connect it to their dynamics, in one of many possible specific contexts. There is flexibility to give the project an algebraic-geometric (e.g. twistor constructions in gauge theory) or differential-geometric flavour (e.g. geometry of the moduli space of harmonic maps), or even a more direct physical slant, with some numerical work (e.g. solitons in exotic superconductors or the Skyrme model of nuclear physics). The successful applicant will join a large and exceptionally vibrant research group, consisting of 14 permanent academic staff, 7 postdocs and over 15 students. The group runs 4 regular seminar series and is a node in 4 regional research networks. All members of the group are internationally recognized experts in their field, sought after as speakers at international research workshops and conferences, and several have been honoured with the award of fellowships or prizes. The group is an active participant in the MAGIC consortium, which provides specialist lecture courses for mathematics postgraduates at a network of Universities.

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

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University&#39;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>&nbsp;in the research information section&nbsp;that the research degree you wish to be considered for is <em><strong>Geometry and Dynamics of Topological Solitons&nbsp;</strong></em>as well as <a href="https://eps.leeds.ac.uk/maths/staff/4079/professor-martin-speight">Professor Martin Speight</a> or <a href="https://eps.leeds.ac.uk/maths/staff/4034/dr-derek-harland">Dr Derek Harland</a> as your proposed supervisor&nbsp;nd in the finance section, please state clearly&nbsp;<em><strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong></em>.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p style="margin-bottom:11px"><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p> <p class="MsoNoSpacing">Applications will be considered after the closing date. &nbsp;Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p>Please note that you must provide the following documents in support of your application by the closing date of 3 April 2024 for&nbsp;Leeds Opportunity Research Scholarship and 8 April 2024 for Leeds Doctoral Scholarship:</p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

<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>&nbsp;&ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a> and <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a> are available to UK applicants (open from October 2023). <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> &ndash;The&nbsp;<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>&nbsp;is available to nationals of China (now closed for 2024/25 entry). The&nbsp;<a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a>&nbsp;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> <p><strong>Important:</strong>&nbsp; Any costs associated with your arrival at the University of Leeds to start your PhD including flights, immigration health surcharge/medical insurance and Visa costs are <strong>not</strong> covered under these studentships.</p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

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

<p>For further information about your application, please contact Doctoral College Admissions by email to&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a></p> <p>For further information about this project, please contact Professor Martin Speight by email to&nbsp;<a href="mailto:j.m.speight@leeds.ac.uk">j.m.speight@leeds.ac.uk</a>&nbsp;or Dr Derek Harland:&nbsp;&nbsp;<a href="mailto:d.g.harland@leeds.ac.uk">d.g.harland@leeds.ac.uk</a>.</p> <p>&nbsp;</p>


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