Professor Dugald Macpherson

Profile

Research interests

I work in model theory (mathematical logic) and adjacent areas of permutation group theory and combinatorics. Particular interests include the following:

1. Model theory of valued fields, from the viewpoint of generalised stability theory -- issues around definability in henselian fields.
2. Generalisations of o-minimality (structure theory arising from restrictions on one-variable definable sets).
3. Model theory of finite and pseudofinite structures -- for example, model-theoretic consequences of asymptotic uniformities on sizes of definable sets.
4. Model theory of groups -- e.g. groups in stable and simple theories, model theory of finite groups.
5. Abstract model theory -- generalisations of stability, connections to combinatorial conditions such as Vapnik-Chervonenkis density.
6. Infinite permutation groups -- often arising as automorphism groups of first order structures.
7. Homogeneous structures in the sense of Fraisse, and omega-categoricity. There are connections to permutation groups and combinatorics, and more recent connections to Ramsey theory, topological dynamics, and constraint satisfaction.

Qualifications

• D.Phil, (Oxford University), 1983

Professional memberships

• London Mathematical Society
• British Logic Colloquium
• European Mathematical Society

Research groups and institutes

• Pure Mathematics
• Logic

Current postgraduate researchers

• Bea Adam-Day
• Francesco Gallinaro
• Rory Ainslie
• Pietro Freni
• Aris Papadopoulos
• Tommy Bernert
• Angus Matthews