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The mathematics of Casimir forces

PGR-P-1331

Key facts

Type of research degree
PhD
Application deadline
Ongoing deadline
Project start date
Sunday 1 October 2023
Country eligibility
International (open to all nationalities, including the UK)
Funding
Competition funded
Supervisors
Professor Alexander Strohmaier
Schools
School of Mathematics
Research groups/institutes
Analysis, Pure Mathematics
<h2 class="heading hide-accessible">Summary</h2>

The PhD project deals with the mathematical structure of the Casimir effect and more generally spectral functions. It has recently been discovered that the Casimir energy can be understood as the trace of a certain operator. This description establishes a link between this quantum field theoretic effect and quantities that have been studied in pure mathematics for a long time. The project it to explore this relation further.<br /> <br /> The Casimir energy has recently been understood as the trace of a certain operator that is locally described by functional calculus of the Laplace operator with certain boundary conditions. This description leads to a precise mathematical definition of the Casimir energy and also allows therefore to apply estimates obtained in spectral geometry to it. Further it leads to a description of the Casimir energy in terms of boundary integral operators, a fact that has been used to speed up the numerical computations. The project is to prove geometric estimates for the Casimir energy with various boundary conditions and relate it to spectral geometry. Background in functional analysis or spectral theory is needed. Background in physics is not required.

<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>and in the research information section&nbsp;that the research degree you wish to be considered for is <em><strong>The Mathematics of Casimir Forces</strong></em> as well as&nbsp;<a href="https://eps.leeds.ac.uk/maths/staff/4080/professor-alexander-strohmaier">Prof. Alexander Strohmaier</a> 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 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 on an ongoing basis. &nbsp;Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. &nbsp;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 at the point you submit your application:</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> <li>Funding information including any alternative sources of funding that you are applying for or if you are able to pay your own fees and maintenance</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 style="margin-bottom:12px"><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>, <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a> and <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship">School of Mathematics Scholarships</a> 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> &ndash;<a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship">The School of Mathematics Scholarships</a> are available to all International applicants.&nbsp; 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. 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 this project, please contact Professor Alexander Strohmaier<br /> e:&nbsp;<a href="mailto:a.strohmaier@leeds.ac.uk">a.strohmaier@leeds.ac.uk</a></p> <p>For further information about your application, please contact Doctoral College Admissions</p> <p>e:&nbsp;&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a></p>


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