Mathematical Interests

 

Complex Systems

I’ve recently become interested in evolution and pattern-formation within various 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, to appear, Arxiv Link)

Tipping Points in Schelling Segregation, with Barmpalias and Lewis-Pye (Journal of Statistical Physics 2014, Arxiv Link)

From Randomness to Order: Unperturbed Schelling Segregation in Two or Three dimensions, with Barmpalias and Lewis-Pye, preprint

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)