Probability Group Members
Members of Staff
Discover more about the members of our Probability Research Group and their diverse interests below.
A common theme throughout much of my work is genealogies. Genealogies record relationships, and transfers, of information across time and space - such as a family tree, or the spread of a news story. I have worked on several situations in which modeling, or analyzing, the large-scale structure of a genealogy is a key issue.
My current main research interest is in random graphs. 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. I have also been interested in variants of preferential attachment which involve a choice mechanism, which may also involve intrinsic properties of the vertices, such as fitness, and in models where the vertices have intrinsic types.
Bas Lodewijks completed his PhD at the University of Bath under the supervision of Marcel Ortgiese, working on randomly grown graphs in random environment and has since worked as a postdoc with Dieter Mitsche at the Institute Camille Jordan in Lyon and Saint-Etienne. More broadly, his expertise and interest lies within probability theory and random graph theory. He currently is a Marie Skłodowska-Curie postdoctoral fellow at the University of Augsburg in Germany working with Markus Heydenreich, as well as an Honorary Lecturer at the University of Sheffield.
I began as a University Teacher in the School in Autumn 2022. Prior to my current role, I worked with Prof. David Applebaum and Dr Jonathon Jordan, studying manifold-valued Feller-Markov processes via their operator semigroups and generators. My approach uses techniques from functional and stochastic analysis, as well as other areas of analysis. Currently I am very interested in the case where the manifold is a Riemannian symmetric space, and particularly in applying the harmonic analysis developed by Harish-Chandra and Sigurður Helgason to determine properties of Feller-Markov semigroups and processes.
My main areas of interest are random trees of the discrete and continuous kind, random graphs, and their local and scaling limits. This has led me to work on a variety of topics including fragmentation-type processes and their family trees, Galton-Watson trees and their limits, Markov Additive Processes, random directed graphs, and random maps.
Since 2019, I have been the Executive Editor of the Applied Probability Trust, based in the School. In addition, I have taken up the post of Executive Manager of the Biometrika Trust since 2022. My Ph.D. was written on the topic of preferential attachment graphs with location. Myself and my supervisor, Dr Jonathan Jordan, proved a number of results on the topics of condensation, coexistence and degree asymptotics. I have been involved in research projects outside of my Ph.D. including work on the cospectrality of graph distance laplacians.
I joined the Department of Computer Science in late 2022. My work is orientated around problems in combinatorics, probability, model theory, and related areas. Prior to Sheffield, I held research visiting positions in Tel Aviv University and Weizmann Institute of Science, Israel. Before this, I was Associate Professor at the department of Discrete Mathematics at Moscow Institute of Physics and Technology.
Current Research Students
Mr Benjamin Andrews
School of Mathematics and Statistics
PhD Student
School of Mathematics and Statistics
PhD Student
My PhD project is on the topic of random graphs and complex networks. I am particularly interested in preferential attachment and its interactions with tournament style growth mechanisms.
Mr Marc Bernard
School of Mathematics and Statistics
PhD Student
School of Mathematics and Statistics
PhD Student
I look forward to researching random graphs and trees, in particular the Galton-Watson process, under the supervision of Robin Stephenson and Jonathan Jordan.
Mr Simon Irons
School of Mathematics and Statistics
PhD Student
School of Mathematics and Statistics
PhD Student
I embarked on a part time PhD in Autumn 2021 under the supervision of Dr Jonathan Jordan. My MSc interests were in analytic number theory, approximation theory, fractal analysis and algebraic graph theory. My dissertation was in the latter using eigenvalues to bound various algebraic graph properties. I plan to investigate problems in random graphs using techniques from spectral analysis.
Mr Navid Mirpoorian
School of Mathematics and Statistics
PhD Student
School of Mathematics and Statistics
PhD Student
My research focuses on the field of probability analysis and its applications to mathematical finance. I am interested in most topics within this and related areas. Especially modeling of financial markets in the presence of arbitrage, investment decision valuation, risk management in financial markets, machine learning in finance, and stochastic portfolio theory.
Retired Staff
Professor David Applebaum
Professor Applebaum graduated with an MA from the University of St Andrews (1979), obtained an MSc in mathematical physics from Nottingham University (1982), and a PhD there in quantum probability (1984). Dave held postdoctoral appointments in Rome, Nottingham and Bielefeld during the next three years. He was appointed as a lecturer at Nottingham Trent University (1987), later becoming a Reader (1994) and Professor (1998). Dave moved to Sheffield as a professor (2004) where he stayed until retirement.
Professor John Biggins
Professor Biggins completed his PhD at Oxford University (1976) on the topic of Asymptotic Properties of the Branching Random Walk. Following his PhD, John was appointed in Sheffield as a lecturer (1976-1992), senior lecturer (1993-94), and professor (1994-2018).