Scheme: Wolfson Research Merit Awards
Organisation: University of Birmingham
Dates: May 2015-Apr 2020
Summary: My main area of research is Combinatorics, in particular Graph Theory. Combinatorics focuses on the study of (finite) structures, which take on discrete values. It underpins the world of information, such as computers, communication networks and the internet. Combinatorics also plays a key role in the study of complex networks arising in nature. In the past, I have developed probabilistic techniques for long-standing problems in this area. One direction I am currently working on is concerned with decomposition and matching problems. Roughly speaking, here the aim is to partition a large structure into many small simple ones. Decomposition problems have a long history going back to the 19th century and have many applications, e.g. to testing and statistical design. Matching problems are of fundamental importance in theoretical computer science. For graphs (where the aim is to partition into suitable pairs of vertices), these are well understood. But the "higher dimensional" version for hypergraphs is computationally intractable and poorly understood from a structural point of view.