Loughborough University

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 fees
  • Alumni 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 £12,000
  • London 10th Anniversary Award

    £5,000 off tuition fees.

    Up to £5,000
  • Loughborough 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 fees
  • Qatari 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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