Mathematics: UKRI CDT PhD Scholarship at Swansea: Tropical Quantum Field Theory

  • Phd
  • Full cost of tuition fees, plus a stipend
  • 12 February 2021
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Mathematics: UKRI CDT Scholarship in Artificial Intelligence, Machine Learning and Advanced Computing: Tropical Quantum Field Theory

This scholarship is funded by UK Research and Innovation (UKRI).

Start date: October 2021

The UK Research and Innovation (UKRI) Centre for Doctoral Training (CDT) in Artificial Intelligence, Machine Learning and Advanced Computing (AIMLAC) aims at forming the next generation of AI innovators across a broad range of STEMM disciplines. The CDT provides advanced multi-disciplinary training in an inclusive, caring and open environment that nurture each individual student to achieve their full potential. Applications are encouraged from candidates from a diverse background that can positively contribute to the future of our society.

Our doctoral training programme is constructed around three research themes:
  • T1: data from large science facilities (particle physics, astronomy, cosmology)
  • T2: biological, health and clinical sciences (medical imaging, electronic health records, bioinformatics)
  • T3: novel mathematical, physical, and computer science approaches (data, hardware, software, algorithms)

  • First supervisor:¬†Professor¬†Biagio Lucini
  • Second supervisor:¬†Dr¬†Yue Ren
  • Third supervisor: Professor¬†Gert Aarts

Department/Institution: Mathematics / Swansea University 

Research theme: T3: novel mathematical, physical and computer science approaches 

Project description:
Quantum Field Theories describe elementary particles and their interactions. The structure of the interaction term plays a crucial role in the definition of the observed physical phenomena. When the interaction is strong, Quantum Field Theories are generally intractable analytically. In these cases, one resorts to numerical computations or to emerging field theories that are easier to tame. Alternative or complementary methods include spatial transformations such as coarse-graining. In this approach, fields describing the particles of the theory are replaced with their integral over a finite region of space whose radius is smaller than the interaction scale. The emerging structure after repeated coarse-graining reveals non-perturbative properties of the theory such as scaling dimensions. An alternative set of transformation can be provided by applications and development of tropical geometry methods. Tropical geometry is the study of properties of shapes when the addition operation is replaced with the minimisation and the multiplication with the addition. Although as a field tropical geometry is still relatively young, insightful applications are emerging in a variety of contexts, such as the financial market, job scheduling and theory of phase transitions. This project will be the first exploration of tropical geometry applications to strongly interacting field theories such as Quantum Chromodynamics, which describes the interaction binding protons and nucleons in nuclei. Together with the development of analytic method, the project will devise a set of techniques and computational algorithms that can be used as a general framework for tropicalisation of Quantum Field Theories. It is anticipated that the corresponding numerical calculations will require high-performance computing capabilities.
Swansea University
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Swansea University

Swansea, is a coastal city and county, officially known as the City and County of Swansea in Wales.

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The typical academic requirement is a minimum of a 2:1 undergraduate degree in biological and health sciences; mathematics and computer science; physics and astronomy or a relevant discipline.

Candidates should be interested in AI and big data challenges, and in (at least) one of the three research themes. You should have an aptitude and ability in computational thinking and methods (as evidenced by a degree in physics and astronomy, medical science, computer science, or mathematics, for instance) including the ability to write software (or willingness to learn it).

This scholarship is open to UK and international candidates (including EU and EEA).


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This scholarship covers the full cost of tuition fees and an annual UKRI standard stipend (currently £15,285 for 2020/21).

Additional funding is available for training, research and conference expenses.


Please visit our website for more information.
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