The Structure and Geometry of Graphs. Graphs are ubiquitous mathematical structures that model relational information such as information flows, transportation networks, and biochemical pathways. It is often desirable to have a geometric representation of a graph. For example, a programmer will better understand a computer program if the flow of information within the program is represented by a visually appealing drawing. The focus of the project will be the interplay between graph structure th ....The Structure and Geometry of Graphs. Graphs are ubiquitous mathematical structures that model relational information such as information flows, transportation networks, and biochemical pathways. It is often desirable to have a geometric representation of a graph. For example, a programmer will better understand a computer program if the flow of information within the program is represented by a visually appealing drawing. The focus of the project will be the interplay between graph structure theory and geometric properties of graphs. Moreover, the project will have significant applications to other area of mathematics and computer science, including computational complexity, analysis of data structures, and three-dimensional information visualisation.Read moreRead less
Finite permutation groups and flag-transitive incidence structures. Mathematics is the enabling discipline for all the sciences and so a strong mathematical research community in Australia provides the foundations for future discoveries in science and technology. By developing new theory for permutation groups, producing a new paradigm for the study of Buekenhout geometries and classifying certain families of flag-transitive incidence structures, we will enhance Australia's leading position in P ....Finite permutation groups and flag-transitive incidence structures. Mathematics is the enabling discipline for all the sciences and so a strong mathematical research community in Australia provides the foundations for future discoveries in science and technology. By developing new theory for permutation groups, producing a new paradigm for the study of Buekenhout geometries and classifying certain families of flag-transitive incidence structures, we will enhance Australia's leading position in Permutation Group Theory, Algebraic Graph Theory and Finite Geometry. This will attract international and Australian postgraduate students and visitors, and strengthen the research activities of Australia by enhancing the collaboration between UWA and leading international universities.Read moreRead less