Geometric Flows

Geometric flows (such as Ricci flow, mean curvature flow, inverse mean curvature flow...) are extremely powerful tools which have been used to solve hard open conjectures such as the Poincar&eacute; conjecture. They have also provided beautiful proofs of important results such as the differentiable sphere theorem and the Penrose inequality. <br /> <br /> Roughly speaking under such a flow, a geometric structure (e.g. a surface or a metric) is deformed over time according to a geometric partial differential equation, hopefully improving the geometric object considered, but possibly also encountering singularities. The analysis and understanding of such singularities guide the application of a given flow. This is an exciting field to work in and significant further applications are to be expected in diverse areas of geometry and topology. <br /> <br /> There are many possible starting points for a project in this area, but the overarching theme of this project will be to investigate and understand the properties of an extrinsic geometric flow such as mean curvature flow, inverse mean curvature flow, Gauss curvature flow or symmetric curvature polynomial flows.

<p><strong>All other Scholarships/Self-funding/Externally Sponsored</strong></p> <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>, in the research information section&nbsp;that the research degree you wish to be considered for is <em><strong>Geometric Flows</strong></em> as well as <a href="https://eps.leeds.ac.uk/maths/staff/10407/dr-ben-lambert">Dr Ben Lambert</a> as your proposed supervisor and in the finance section, please state clearly <em><strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong></em>.</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>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 after the closing date. &nbsp;Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. 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 in support of your application by the closing date of 3 April 2024 for Leeds Opportunity Research Scholarship or&nbsp;8 April 2024 for Leeds Doctoral Scholarship:</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> </ul>

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.

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.

<p><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>,&nbsp;<a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a>&nbsp;and <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship">School of Mathematics Scholarships</a><span style="font-size:11.0pt"><span style="line-height:107%"><span style="font-family:&quot;Calibri&quot;,sans-serif">&nbsp;</span></span></span>are available to UK applicants (open from October 2023). <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;&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 (now closed for 2024/25 entry). 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><em><strong>Important:&nbsp;</strong></em> 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 <em><strong>not</strong></em> covered under this studentship.</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>

<p>For general enquiries about applications, contact our admissions team by email to&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a><br /> For questions about the research project, contact Dr. Ben Lambert by email to&nbsp;<a href="mailto:b.s.lambert@leeds.ac.uk">b.s.lambert@leeds.ac.uk</a></p>