Dr Joshua Erde BA MA MMath PhD

• Habilitation, Graz University of Technology (2021)
• Habilitation, University of Hamburg (2020)
• PhD in Mathematics, University of Cambridge (2014)
• MMath, University of Cambridge (2010)
• MA (Cantab) in Mathematics, University of Cambridge (2009)

Joshua studied for his BA/MMath and PhD at the University of Cambridge from 2006-2014. From 2014 to 2019 he was a postdoctoral researcher at the University of Hamburg, supported for two years as a fellow of the Alexander von Humboldt research institute. From 2019 to 2025, he was a non-tenured Assistant Professor at Graz University of Technology. Since August 2025, he has been an Assistant Professor in the School of Mathematics at the University of Birmingham.

Semester 2

• LH/LM Communications Theory

Joshua is interested in supervising PhD students in Combinatorics. Please get in touch via email.

Research Themes

• Probabilistic combinatorics
• High-dimensional random structures and processes
• Structural graph theory
• Infinitary combinatorics
• Combinatorial games

Research activity

Joshua is interested in random graph models and random processes on graphs, in particular those where the underlying model has some sparse rigid geometric or algebraic structure.

For example, much is known about the evolution of the structure of the classic binomial random graph model. Much less is known when for broader classes of random subgraphs, although results suggest that the behaviour of the binomial random graphs is `universal’ when the host graph is sufficiently ‘well-structured’.

Joshua’s recent results in this area include bounding parameters such as the diameter or circumference of random subgraphs of graphs with a high-dimensional product structure, such as the hypercube.