Dispersionless integrable systems in 2+1 dimensions

Program Overview

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The PhD in Dispersionless Integrable Systems in 2+1 Dimensions at Loughborough University offers a research-intensive program in integrability theory and computational techniques. Students will gain expertise in advanced mathematical analysis, integrable systems, and dispersionless deformations, preparing them for careers in academia, research, or the private sector. The program features a combination of taught modules and an individual research project supervised by world-leading experts.

Program Outline

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Degree Overview:

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Name:

PhD in Dispersionless Integrable Systems in 2+1 Dimensions

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Duration:

3 years (full-time) or 6 years (part-time)

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Start Date:

October 2024

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Objectives:

• Train graduates to be independent scientists able to:
• Conduct original research on applications of integrable systems in various disciplines
• Contribute to advances in integrability theory and computational techniques
• Publish results in peer-reviewed journals
• Prepare graduates for careers in academia, research and development institutions, or in the private sector

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Program Description:

This program provides a unique opportunity to study dispersionless integrable systems in a research-intensive environment. Students will gain in-depth knowledge of theoretical and computational methods related to integrability in various areas of pure and applied mathematics. They will conduct original research under the supervision of world-leading experts and develop strong analytical and problem-solving skills.

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Outline:

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Program Content:

• Advanced mathematical analysis
• Integrable systems and hydrodynamic reductions
• Hypergeometric functions and modular forms
• Dispersionless deformations of integrable systems
• Computational techniques for integrability

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Structure:

The program includes a combination of:

• Taught modules
• Individual research project

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Taught Modules:

• Introduction to integrable systems
• Integrable systems in 2+1 dimensions
• Hydrodynamic reductions
• Hypergeometric functions and modular forms
• Dispersionless deformations
• Advanced computational methods for integrability

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Individual Research Project:

Under the supervision of a faculty member, students will conduct independent research on a specific topic related to dispersionless integrable systems. They will present their findings in a dissertation and defend it in a viva voce examination.

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Assessment:

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Taught Modules:

• Continuous assessment through coursework and assignments
• End-of-module examinations

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Individual Research Project:

• Progress reports submitted throughout the research
• Dissertation
• Viva voce examination

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Teaching:

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Teaching Methods:

• Lectures
• Seminars
• Workshops
• Individual supervision meetings

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Faculty:

• Internationally renowned experts in integrable systems and related fields

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Unique Approaches:

• Research-led teaching
• Access to advanced computational facilities
• Strong emphasis on individual mentorship and research guidance

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Careers:

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Potential Career Paths:

• Academia (postdoctoral positions, research fellowships, faculty positions)
• Research and development institutions (government labs, private companies)
• Private sector (finance, technology, consulting)

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Career Outcomes:

Graduates will develop the knowledge, skills, and networks to pursue successful careers in various fields where mathematical modeling and analysis are key.

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Other:

• The program is particularly suitable for students with a strong background in mathematics and an interest in research.
• The research project allows students to specialize in a specific area of interest related to dispersionless integrable systems.
• Graduates will have the opportunity to present their research at international conferences and workshops.

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Fees and Funding:

• Full-time UK student: £4,712 per year
• Full-time international student: £20,250 per year

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Admission Requirements:

• Applicants should have, or expect to achieve, a 2.1 Honours degree in mathematics.
• Other entry requirements may apply.
• The application deadline is 1st July 2024.

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UK fee: £4,712 Full-time degree per annum International fee: £20,250 Full-time degree per annum University fees and charges can be paid in advance and there are several methods of payment, including online payments and payment by instalment. Fees are reviewed annually and are likely to increase to take into account inflationary pressures.