
Lieb-Thirring inequalities for Generalized Indefinite Strings
Loughborough UniversityLoughborough, United Kingdom
Course overview
Lieb–Thirring inequalities provide upper bounds on the negative eigenvalues of Schrödinger operators in terms of the potential. Such inequalities have important applications in quantum mechanics, in particular for establishing the stability of matter. The aim of this project is to establish analogue inequalities for general second-order ordinary differential equations in the form of generalized indefinite strings and canonical systems.
Work in this area will involve a combination of advanced tools from various areas of analysis. 94% of Loughborough’s research impact is rated world-leading or internationally excellent. REF 2021
Key highlights
- Research project extending Lieb–Thirring inequalities to generalized indefinite strings
- Covers second-order differential equations and canonical systems
- Combines advanced tools from several areas of mathematical analysis
- Links to quantum mechanics applications, including stability of matter
- 94% of research impact rated world-leading or internationally excellent (REF 2021)
Entry requirements
- Degree: 2:1 — 2:1 in mathematics-related degree
Scholarships
Alumni Bursary
10% of tuition fees which will be credited to the student’s tuition fee account.
Up to 10% of feesAlumni Discount
UK students: £1,500 tuition fee discount for one academic year. International students: £3,000 tuition fee discount for one academic year.
Care Leaver's Scholarship
Excellence Scholarships
UK students: £3,000 off tuition fees; International students: £6,000 off tuition fees which will be credited to the student’s tuition fee account.
International Sports Student Postgraduate Bursary
Our International Sports Student Postgraduate Bursary offers a £12,000 tuition fee discount (set against the tuition fees of your chosen postgraduate taught programme ONLY).
Up to £12,000London 10th Anniversary Award
£5,000 off tuition fees.
Up to £5,000Loughborough Business School Scholarship
£1,500 (UK students) and £3,000 (international students) off tuition fees which will be credited to the student’s tuition fee account.
MBA Progress with Purpose Scholarship
50% of tuition fees which will be credited to the student’s tuition fee account.
Up to 50% of feesQatari Ghanim Al-Muftah Excellence Scholarship
Careers this course leads to
- Postdoctoral researcher in mathematics
- University lecturer in mathematics
- Mathematical physicist
- Quantitative analyst
- Research scientist
Cost of study
UK/Home: £5,238 | International: £23,100
Admission
Applications are made through AHZ at no cost. Share your transcripts, English test scores and personal statement, and your AHZ Counsellor will review your profile, submit your application to Loughborough University, and guide you through interview, offer, CAS and visa — right up to enrolment.
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