PhD Studentship - Truncated Moment Problems and the Quantum Classical Divide

Award summary 100% fees covered, and a minimum tax-free annual living allowance of £19,237 (2024/25 UKRI rate). Overview Given a closed set K in R^d and a truncated multisequence of real numbers the TKMP (truncated K-moment problem) entails determining whether or not there exists a positive Borel measure supported on K, whose initial power moments are the given truncated multisequence. In this case, we say that the given multisequence has a K-representing measure. In general, the TKMP is intractable. Turning now to physics, if we interpret the given multisequence as the observed outcomes of a set of experiments and K as reflecting the structure inherent to the physical system under investigation, the TKMP maps onto the question of whether the set of experimental outcomes can be derived from an underlying probability distribution. Since Bell, this question has been central to discussions on the meaning and interpretation of quantum theory because, whereas classical theories can couched in such probabilistic terms, quantum theory cannot. In this project we will be investigating concrete solutions of the TKMP when K is a finite lattice and immediately using the mathematical solution to address Bell-type problems in Quantum Physics. Number of awards: 1 Start date: 16 September 2024 Award duration: 3.5 years Sponsor: EPSRC Doctoral Training Partnerships (DTP) Supervisors: Dr David Kimsey Eligibility criteria You must have, or expect to gain, a minimum 2:1 Honours degree or international equivalent in a subject relevant to the proposed PhD project (inc. computing, mathematics, engineering etc.). Enthusiasm for research, the ability to think and work independently, excellent analytical skills and strong verbal and written communication skills are also essential requirements. Home and international applicants (inc. EU) are welcome to apply and if successful will receive a full studentship. Applicants whose first language is not English require an IELTS score of 6.5 overall with a minimum of 5.5 in all sub-skills. International applicants may require an ATAS (Academic Technology Approval Scheme) clearance certificate prior to obtaining their visa and to study on this programme. How to apply You must apply through the University’s Apply to Newcastle Portal Once registered select ‘Create a Postgraduate Application’. Use ‘Course Search’ to identify your programme of study: Search for the ‘Course Title’ using the programme code: 8080F Research Area: Pure Mathematics Select ‘PhD Mathematics (full time) - Mathematics' with research area ‘pure' as the programme of study You will then need to provide the following information in the ‘Further Details’ section: A ‘Personal Statement’ (this is a mandatory field) - upload a document or write a statement directly in to the application form The studentship code MSP084 in the ‘Studentship/Partnership Reference’ field When prompted for how you are providing your research proposal - select ‘Write Proposal’. You should then type in the title of the research project from this advert. You do not need to upload a research proposal. You must submit one application per studentship, you cannot apply for multiple studentships on one application. Contact details Dr David Kimsey, School of Mathematics, Statistics and Physics david.kimsey@newcastle.ac.uk