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# Mutation in cluster algebras and in oriented graphs

PGR-P-630

## Key facts

Type of research degree
PhD
Application deadline
Ongoing deadline
Country eligibility
International (open to all nationalities, including the UK)
Funding
Non-funded
Supervisors
Professor Karin Baur
Schools
School of Mathematics
Research groups/institutes
Pure Mathematics
<h2 class="heading hide-accessible">Summary</h2>

The interplay between algebra, geometry and combinatorics is a major focus of my current research. We take surfaces obtained from gluing polygons and use them to define and explore algebraic structures such as cluster categories, a young and thriving field with links to many other areas in Mathematics. The interactions between geometry and algebra are illustrated by the classical theorems of Pythagoras and Ptolemy. They characterise geometric properties of a polygon via algebraic equations. Ptolemy&amp;rsquo;s theorem gives us information on one diagonal in the quadrilateral in terms of the other. We call the relation between the two diagonals a flip and its algebraic effect mutation, a key notion in cluster categories. One of our aims is to determine this mutation in associated categories, thus using elementary geometry to approach involved algebraic structures. Since mutation is a phenomenon present in many research areas in Pure Mathematics, understanding various aspects of mutation will illuminate and advance other areas.

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

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="http://www.leeds.ac.uk/rsa/prospective_students/apply/I_want_to_apply.html">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;Mutation in cluster algebras and in oriented graphs&rsquo; as well as&nbsp;<a href="https://eps.leeds.ac.uk/maths/staff/4250/professor-karin-baur-">Professor Karin Baur</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><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> <p>&nbsp;</p>

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

<p>For further information regarding your application, please contact Doctoral College Admissions by email:&nbsp;&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a>&nbsp;or by telephone: + 44 (0) 113 343 5057.</p> <p>For further information regarding the project,&nbsp;please contact Professor Karin&nbsp;Baur by&nbsp;email:&nbsp;<a href="mailto:pmtkb@leeds.ac.uk">pmtkb@leeds.ac.uk</a><br /> &nbsp;</p>

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