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Spectral geometry

PGR-P-236

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
Dr Gerasim Kokarev
Schools
School of Mathematics
Research groups/institutes
Pure Mathematics
<h2 class="heading hide-accessible">Summary</h2>

Spectral geometry lies at the intersection of differential geometry, partial differential equations, and analysis. To a large extent it is motivated by questions originating in the study of real-life phenomena, such as vibration, heat propagation, oscilation of fluids, and quantum mechanical effects.<br /> <br /> For example a model question, posed by Mark Kac half a century ago, is &amp;quot;Can one hear the shape of a drum?&amp;quot; The challenge is to understand the geometry of an idealized drum from the set of its vibration frequences, that is the Laplace eigenvalues. Kac&amp;rsquo;s question is closely linked to other topics in spectral geometry, including shape optimization, spectral asymptotics, and spectral invariants.<br /> <br /> There are many starting points for a project in this general area, including isoperimetric inequalities, eigenvalue problems and spectral invariants in Riemannian geometry, eigenvalue problems in the minimal surface theory, and extremal eigenvalue problems.

<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;Spectral geometry&rsquo; as well as&nbsp;<a href="https://physicalsciences.leeds.ac.uk/staff/49/dr-gerasim-kokarev">Dr Gerasim Kokarev</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 are welcome to apply.</strong></p> <p><strong>UK&nbsp;students</strong>&nbsp;&ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/138-leeds-doctoral-scholarships-2021-january-deadline">Leeds Doctoral Scholarship (January deadline)</a>&nbsp;and the&nbsp;<a href="https://phd.leeds.ac.uk/funding/142-william-wright-smith-scholarship-2021">William Wright Smith Scholarship&nbsp;</a>are available to UK applicants. &nbsp;<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 students</strong>&nbsp;&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. 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.&nbsp; <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&nbsp;email:&nbsp;<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 Gerasim Kokarev by email:&nbsp;&nbsp;<a href="mailto:G.Kokarev@leeds.ac.uk">G.Kokarev@leeds.ac.uk</a></p>


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