PhD Studentship - Weak and Strong Saturation in Graphs

Do you enjoy studying and developing probabilistic and algebraic techniques for solving combinatorial problems? The Verification group in the Department of Computer Science, The University of Sheffield, is welcoming applications to a PhD position in “Weak and strong saturation in graphs”. Maksim Zhukovskii will be the main supervisor of the PhD student.

Weak saturation can be seen as the minimum number of edges needed to activate all edges of a graph by a monotone cellular automaton known as a bootstrap percolation process. In general settings not much is known about this parameter. The most well-developed methods of studying this parameter are algebraic. However, they work well only for highly symmetric structures. The aim of the project is to develop these techniques, transfer results to random graphs, and study the `strong version’ of the saturation number.

I am looking for a motivated PhD student to join the Department of Computer Science, The University of Sheffield www.sheffield.ac.uk/dcs. The project aims to improve known bounds for saturation numbers in complete graphs and random graphs, as well as to develop algebraic and combinatorial techniques for solving problems on graph bootstrap percolation.

The start date is 1^st September 2023.

About the Department and Research Group:

99 percent of our research is rated in the highest two categories in the REF 2021, meaning it is classed as world-leading or internationally excellent. We are rated as 8th nationally for the quality of our research environment, showing that the Department of Computer Science is a vibrant and progressive place to undertake research.

Candidate requirements:

Applicants should have a relevant master’s qualification (in mathematics or computer science). Good knowledge of discrete mathematics and probability is expected. A serious interest in pursuing fundamental research is necessary.

Applicants must also ensure that they fulfil the English language requirements for postgraduate students, details of which can be found here: www.sheffield.ac.uk/postgraduate/english-language.

How to apply:

To apply for a PhD studentship, applications must be made directly to the University of Sheffield using the Postgraduate Online Application Form. Make sure you name Maksim Zhukovskii as your proposed supervisor.

Information on what documents are required and a link to the application form can be found here - www.sheffield.ac.uk/postgraduate/phd/apply/applying

The form has comprehensive instructions for you to follow, and pop-up help is available. Your research proposal should:

• Be no longer than 4 A4 pages, include references
• Outline your reasons for applying for this studentship
• Explain how you would approach the research, including details of your skills and

Experience in the topic area

Funding:

Funding is available for this position, paying the tuition fee (UK fee level) and a stipend at the standard UK Research rate (£17,668 for 2022-23). International students are eligible to apply if they can self-fund the difference between the home and overseas fee. However, funding to cover the additional cost of the overseas tuition fee may be available for exceptional international applicants.

Advert information