Extremal hypergraph theory
Extremal graph theory is an important and active area of combinatorics, devoted to the study of graphs which are extremal amongst those satisfying some given property. For example, which graph(s) have the most edges amongst all graphs on n vertices which do not contain a triangle (see Mantel’s theorem)? What is the weakest minimum degree condition which ensures the existence of a Hamilton cycle in a graph (see Dirac’s theorem)? Whilst the aforementioned theorems are classical, this topic is an area of rapid development, particularly with regard to hypergraph analogues of these questions. Recently powerful tools such as the absorbing method and hypergraph blow-up lemma have been established, and give new lines of approaching the many important conjectures and open problems in the field.
The University of Birmingham has a vibrant and diverse research group in Combinatorics and Graph theory. Indeed, the group has 8 permanent members of staff as well as a number of research fellows and postgraduate students. More details about the group can be found at: http://www.birmingham.ac.uk/research/activity/mathematics/pure-maths/combinatorics.aspx
To find out more about studying for a PhD at the University of Birmingham, including full details of the research undertaken in each school, the funding opportunities for each subject, and guidance on making your application, you can now order your copy of the new Doctoral Research Prospectus at: www.birmingham.ac.uk/students/drp.aspx
This research project is one of several projects at this institution. It is in competition for funding with one or more of these projects. Usually the project which receives the best applicant will be awarded the funding. The funding is only available to UK citizens who are normally resident in the UK or those who have been resident in the UK for 3 years or more.
Non-UK Students: If you have the correct qualifications and access to your own funding, either from your home country or your own finances, your application to work on this project will be considered.
How good is research at University of Birmingham in Mathematical Sciences?
FTE Category A staff submitted: 40.00
Research output data provided by the Research Excellence Framework (REF)
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