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Covariant Spectral Theory

PGR-P-688

Key facts

Type of research degree
PhD
Application deadline
Ongoing deadline
Country eligibility
International (open to all nationalities, including the UK)
Funding
Competition funded
Source of funding
University of Leeds
Supervisors
Dr Vladimir Kisil
Schools
School of Mathematics
Research groups/institutes
Pure Mathematics
<h2 class="heading hide-accessible">Summary</h2>

Families of invertible transformations of geometric sets are rich sources of interesting and important groups. Properties of geometric objects, which are invariant under such transformations, are subject of geometry according to the Erlangen Programme of Felix Klein. Transformations of sets can be naturally extended to actions on linear functional spaces defined on those sets, so we obtain linear representations of groups. There are many questions in analytic function theory which are greatly simplified by a consideration of an appropriate group representation. Finally, we can consider actions of the same groups on operators or, more generally, on Banach algebras and other non-commutative sets. There are oftenly intertwining operators linking group actions on non-commutative spaces and linear spaces of functions. Depending on the direction they act those intertwining operators are known as functional calculi or functional models. A study of covariant properties of functional calculi provide valuable characterisation of operator spaces in geometrical terms. Thus it is a natural extension of the Erlangen programme to non-commutative sets.

<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;Covariant Spectral Theory&rsquo; as well as&nbsp;<a href="https://eps.leeds.ac.uk/maths/staff/4048/dr-vladimir-v-kisil">Dr Vladimir V Kisil</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:&nbsp; e:&nbsp;&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a>&nbsp;or t:&nbsp;+ 44 (0) 113 343 5057.</p> <p>For further information regarding the project,&nbsp;please contact Dr Vladimir V. Kisil:&nbsp;e: <a href="mailto:V.Kisil@leeds.ac.uk">V.Kisil</a><a href="mailto:EMAIL@leeds.ac.uk">@leeds.ac.uk</a>&nbsp;or t: +44 (0)113 343 5173.</p>


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