Mathematics: Fully Funded PhD at Swansea in Topological Data Analysis for Biomedical Data

  • Phd
  • Full cost of UK/EU tuition fees, plus a stipend
  • 28 February 2020

Mathematics: Fully Funded PhD Scholarship in Topological Data Analysis for Biomedical Data

Project Supervisors:

  • Supervisor 1:¬†Jeffrey Giansiracusa
  • Supervisor 2:¬†Yue Ren

Project description:

As part of the major Oxford-Swansea-Liverpool Centre for Topological Data Analysis (funded by EPSRC grant EP/R018472/1), we are looking for a PhD student to join the Swansea team (consisting of 5 permanent core members and multiple postdocs and PhD students) in investigating applications of topology to data science and physics.

The precise focus of this project will be to develop and implement new computational topology methods for a diverse range of data-analysis problems, driven by challenges from biomedical science, economics, and physics. Principal tools will include persistent homology, Mapper / Ball Mapper, and Hodge theory on graphs. The project will involve a mixture of theoretical and computational work (both using existing tools, and writing new code).

The successful applicant will work within the Computational Foundry and will be a part of the Swansea Science Doctoral Training Centre and have access to an array of training and networking opportunities through two Centres for Doctoral Training that we host.

Our interdisciplinary team currently consists of the following members:

  • Professor Jeffrey Giansiracusa - an expert in topology and tropical algebraic geometry.
  • Professor Biagio Lucini - an expert in computational physics and quantum theory, and machine learning
  • Dr Pawel Dlotko - an expert in applied and computational topology and data analysis.
  • Dr Yue Ren - UKRI Future Leader Fellow with interests in computational geometry, tropical geometry, and machine learning.
  • Dr John Harvey ‚Äď Daphne Jackson Fellow with interests in computational geometry and statistics.
  • Dr Farzad Fathizaddeh ‚Äď S√™r Cymru Fellow with research interests in noncommutative geometry and data science
  • Dr Tak-Shing Chan - Research interests in topological data analysis and machine learning.
  • Multiple PhD students

Background on the Centre for Topological Data Analysis:

Modern science and technology generates data at an unprecedented rate. A major challenge is that this data is often complex, high dimensional, may include temporal and/or spatial information. The "shape" of the data can be important but it is difficult to extract and quantify it using standard machine learning or statistical techniques. For example, an image of blood vessels near a tumour looks very different than an image of healthy blood vessels; statistics alone cannot quantify this difference and the new shape analysis methods are required.

The focus of the work of this Centre is to study the shape of data, through the development of new mathematics and algorithms, and build on existing data science techniques in order to obtain and interpret the shape of data. A theoretical field of mathematics that enables the study of shapes is geometry and topology. The ability to quantify the shape of complicated objects is only possible with advanced mathematics and algorithms. The field known as topological data analysis (TDA), enables one to use methods of topology and geometry to study the shape of data. In particular, a method within TDA known as persistent homology provides a summary of the shape of the data (e.g., features such as holes) at multiple scales. A key success of persistent homology is the ability to provide robust results, even if the data are noisy. There are theoretical and computational challenges in the application of these algorithms to large scale, real-world data.

The aim of this Centre is to build on current persistent homology tools, extending it theoretically, computationally, and adapting it for practical applications. Our core team is composed of experts in pure and applied mathematicians, computer scientists, and statisticians whose combined expertise covers cutting edge pure mathematics, mathematical modelling, algorithm design and data analysis. This core team will work closely with our collaborators in a range of scientific and industrial domains.

Swansea University
This is a scholarship by

Swansea University

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

Eligibility

Candidates must have a first or upper second class honours undergraduate degree (or equivalent) or a Master's degree, in a relevant discipline.

For candidates whose first language is not English, we require IELTS 6.0 (with 5.5 in each component) or equivalent. Please visit our website for a list of acceptable English Language tests.

Please note that international (non-EU) students are welcome to apply, but a portion of the stipend would have to be used to cover the difference between UK/EU fees and full international fees.

Benefits

This is a three-year fully funded Swansea University scholarship, which covers UK/EU tuition fees plus an annual stipend of £15,245. Additional funding is available to cover costs such as research consumables, training, conferences and travel.

Please note that international (non-EU) students are welcome to apply, but a portion of the stipend would have to be used to cover the difference between UK/EU fees and full international fees.

Application

Please visit our website for more information.

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