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Geometry and Dynamics of Topological Solitons

PGR-P-207

Key facts

Type of research degree
PhD
Application deadline
Ongoing deadline
Country eligibility
International (open to all nationalities, including the UK)
Funding
Competition funded
Supervisors
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 hide-accessible">Full description</h2>

<p>The earliest start date for this project is 1 October 2020.</p>

<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/info/130206/applying/91/applying_for_research_degrees">University&#39;s website</a>. Please state clearly in the research information section&nbsp;that the research degree you wish to be considered for is &lsquo;Geometry and Dynamics of Topological Solitons&rsquo; as well as&nbsp;<a href="https://physicalsciences.leeds.ac.uk/staff/79/professor-martin-speight">Professor Martin Speight</a>&nbsp;as your proposed supervisor.</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><em>We welcome applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.</em></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-Funding Students</strong></p> <p><strong>Funding Eligibility</strong></p> <p><strong>UK/EU</strong> &ndash;&nbsp;Leeds Doctoral Scholarship Award paying Academic Fees and Maintenance matching EPSRC rate of &pound;15,009 per year for 3 years, School of Mathematics Scholarship award paying Academic Fees and Maintenance matching EPSRC rate of &pound;15,009 per year for 3 years.&nbsp; Alumni Bursary is available to previous University of Leeds graduates offering 10% discount on Academic Fees.</p> <p><strong>International Students</strong> &ndash;&nbsp;China Scholarship Council-University of Leeds Scholarship Award paying Academic Fees for 3 years,&nbsp;School of Mathematics Scholarship award paying Academic Fees for 3 years, Commonwealth Scholarship and Commonwealth Split Site Scholarships.&nbsp; Alumni Bursary is available to previous University of Leeds graduates offering 10% discount on Academic Fees.</p>

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

<p>For further information please contact Doctoral College Admissions by&nbsp;email:&nbsp;<a href="mailto:EMAIL@leeds.ac.uk">m</a><a href="mailto:maps.pgr.admissions@leeds.ac.uk">aps.pgr.admissions@leeds.ac.uk</a>, or by telephone: +44 (0)113 343 5057</p> <p>For further information regarding the project, please contact Professor Martin Speight by email:&nbsp;&nbsp;<a href="mailto:J.M.Speight@leeds.ac.uk">J.M.Speight@leeds.ac.uk</a></p>


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