Network scientists employ various models to mimic real world networks such as the world-wide web. I have recently started a project analyzing the infinite limits of these types of models.
• Preferential Attachment Processes Approaching The Rado Multigraph; submitted. ArXiv Link.
I am interested in evolution and pattern-formation within nonlinear and complex systems. With Andy Lewis-Pye and George Barmpalias, I have been analyzing a fascinating model of racial segregation first proposed by the Nobel-Prize winning economist Thomas Schelling:
• Digital Morphogenesis via Schelling Segregation, with Barmpalias and Lewis-Pye (FOCS 2014: 156-165, Arxiv Link)
• Tipping Points in Schelling Segregation, with Barmpalias and Lewis-Pye (Journal of Statistical Physics, February 2015, Volume 158, Issue 4, pp 806-852, Arxiv Link)
• From Randomness to Order: Unperturbed Schelling Segregation in Two or Three dimensions, with Barmpalias and Lewis-Pye, Submitted. Arxiv Link)
My background is in Model Theory, a branch of mathematical logic, and its applications to algebra. I’m interested in simple theories, geometric stability theory, the model theory of groups and fields, and the interplay between these.
• Dimension And Measure In Finite First Order Structures
PhD thesis, University of Leeds, 2005, (pdf)
• Asymptotic Classes Of Finite Structures
Journal Of Symbolic Logic, 72, 2, 2007, pp. 418-438; (pdf)
• A Survey Of Asymptotic Classes and Measurable Structures (with Dugald Macpherson)
in Model Theory with Applications to Algebra and Analysis Volume 2 (Cambridge University Press, 2008) (pdf)
• Measurable Groups of Low Dimension (with Mark Ryten)
Mathematical Logic Quarterly 54, No 4, 374-386 (2008)
• Groups in supersimple and pseudofinite theories (with Dugald Macpherson, Eric Jaligot, Mark Ryten) Proceedings of the LMS, Vol 103, Part 6, 1049-1082. (pdf)
• Slides from my talk “An amateur’s guide to concrete incompleteness” (commentary and slides)
• Galois Maps, Measure, and Generic Automorphisms in Strongly Minimal Sets (pdf)