## General informationI am a Lecturer in the School of Mathematics and
Statistics at the University of Sheffield.
I obtained my DPhil from the
Mathematical Institute in the University of Oxford, associated with
St. Anne's College and working with Neil
O'Connell and Ben Hambly; my thesis (PDF format) was titled Useful link: MathSciNet Probability in the North East 2018 Easter Probability Meeting at Sheffield ## Random graphsMy current main research interest is in random graphs. The theory of random graphs dates back to Erdős and Rényi in 1959, but there has been an explosion of interest since the late 1990s, with applications arising in fields such as computer science and biology. One family of models I have been particularly interested in is the so-called preferential attachment models based on the original model of Barabási and Albert, in which new vertices join the graph and are connected to existing vertices; existing vertices are more likely to pick up new neighbours if they already have high degree. These models tend to show an asymptotically power law (or "scale free") degree sequence. Recently, I have been particularly interested in variations on this model with a geometric element, with two papers, one in "uniform" metric spaces, and one in a more general setting. I have also looked at other models of random graphs which may show some similar features, such as preferential duplication and random reproducing graphs. Some of the pictures below show some of the models I have worked on. From 2006 to 2010 I was involved with the Amorph project. I am available to supervise PhD topics in the general area of random graphs, in particular where related to the models discussed above. I may also consider supervising topics related to random graphs with a more applied flavour, possibly in partnership with other researchers interested in this area. ## FractalsI have also been interested in fractals, in particular random fractals and the spectral properties of fractal graphs. Random fractal graphs were a large part of my PhD thesis (and see also the paper on the "series-parallel network"). The spectral properties of Laplacians (defined as matrices closely related to the generator matrices of continuous time random walks) of some fractal graphs (such as those related to the Sierpiński gasket) show a property called "spectral decimation", by which the eigenvalues of one stage in the construction may be found by solving equations of the form ## Other pagesTeaching PagePersonal Page ## Contacting meMy department address is Department of Probability and Statistics,University of Sheffield, Hicks Building, Hounsfield Road, Sheffield. S3 7RH Telephone: +44 (0)114 222 3873 email: jonathan.jordan@sheffield.ac.uk |

Last updated 24 August 2017.