Topics in Ergodic Theory and Fractal Geometry
| Program start date | Application deadline |
| 2024-04-01 | - |
| 2024-07-01 | - |
Program Overview
This PhD program explores invariant sets and measures in iterated function systems, combining Ergodic Theory and Fractal Geometry. It aims to understand the cardinality and complexity of codings for points in invariant sets and the number theoretic properties of typical points within them. The program's research impact is highly rated, with 94% of Loughborough's research being world-leading or internationally excellent.
Program Outline
The project lies at the intersection of Ergodic Theory and Fractal Geometry. The goal is to approach this topic from various angles, including:
- Understanding the cardinality and complexity of the set of codings for a point in the invariant set.
- Understanding the number theoretic properties of a typical point belonging to the invariant set. This goal can be approached from various angles. Specific problems include understanding the cardinality and complexity of the set of codings for a point in the invariant set or understanding the number theoretic properties of a typical point belonging to the invariant set. This project lies at the intersection of Ergodic Theory and Fractal Geometry. 94% of Loughborough’s research impact is rated world-leading or internationally excellent. REF 2021
Loughborough University
Overview:
Loughborough University is a public research university located in Loughborough, Leicestershire, England. It is renowned for its strong academic programs, particularly in sports science, engineering, and business. The university boasts a vibrant campus life and a strong focus on research and innovation.
Student Life and Campus Experience:
Loughborough University offers a diverse and engaging campus experience. Students can participate in a wide range of extracurricular activities, including sports, societies, and volunteering opportunities. The university has a strong sporting heritage and is home to world-class facilities. Students can also enjoy a vibrant social scene with numerous bars, restaurants, and events happening on campus.
Key Reasons to Study There:
World-class facilities:
Loughborough University boasts state-of-the-art facilities, including a dedicated sports village, a modern library, and cutting-edge research labs.Strong academic reputation:
The university is consistently ranked among the top universities in the UK for its academic excellence.Vibrant campus life:
Students can enjoy a lively and diverse campus community with numerous opportunities for social interaction and personal development.Focus on research and innovation:
Loughborough University is a leading research institution, with a strong focus on tackling real-world challenges.Excellent career prospects:
Graduates from Loughborough University are highly sought after by employers, with strong career prospects in various fields.Academic Programs:
Loughborough University offers a wide range of undergraduate and postgraduate programs across various disciplines, including:
Engineering:
Aerospace, Chemical, Civil, Electrical, Mechanical, and more.Business and Economics:
Accounting, Finance, Management, Marketing, and more.Sport Science:
Exercise Science, Sports Coaching, Sports Management, and more.Humanities and Social Sciences:
Psychology, Sociology, History, and more.Science and Technology:
Chemistry, Physics, Computer Science, and more.Other:
Loughborough University has a strong commitment to sustainability and social responsibility. The university is actively working towards achieving net-zero carbon emissions and promoting inclusivity and diversity within its community.
Entry requirements
United Kingdom
- Applicants should have, or expect to achieve, a 2:1 Honours degree (or equivalent) in Mathematics or a related subject.
July 2024 programme start date
- Only available to international applicants, due to ATAS approval and visa application timescales.
Language Proficiency Requirements
- English language requirements
- Applicants must meet the minimum English language requirements.
