### Mathematical Interests

### Random Networks

I have recently started a project analyzing the infinite limits of models of random networks.

• *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.

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.

### Some papers and pre-prints

• *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)