Mathematical Interests
I work 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.
Papers
Dimension And Measure In Finite First Order Structures
PhD thesis, University of Leeds, 2005, downloadable here as a pdf file.
Asymptotic Classes Of Finite Structures
Journal Of Symbolic Logic, 72, 2, 2007, pp. 418-438; downloadable here as a pdf file.
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)
Measurable Groups of Low Dimension (with Mark Ryten)
Mathematical Logic Quarterly 54, No 4, 374-386 (2008)
Pre-Prints
(These are liable to be changed without warning.)
PAC Substructures Of Strongly Minimal Sets (with Bijan Afshordel)
Lecture Notes
Galois Maps, Measure, and Generic Automorphisms in Strongly Minimal Sets downloadable here as a pdf file.