Random Networks

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.

Complex Systems

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

Minority population in the one-dimensional Schelling model of segregation, with Barmpalias and Lewis-Pye, Submitted. Arxiv Link

See also my blog-posts (1 & 2) on the subject.

Mathematical Logic

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)

Lecture Notes

• 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)