# School of Mathematics

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## Prof H Dugald Macpherson

Professor of Pure Mathematics

Pure Mathematics

### Contact details

Room: Satellite 10.25

Tel: +44 (0)113 3435166

Email: H.D.MacPherson @ leeds.ac.uk

### Keywords

Model theory

Stability theory

O-minimal

Pseudofinite

Infinite permutation group

Homogeneous structure

Valued field

Vapnik-Chervonenkis density

## 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-Chevonenkis density.

6. Infinite permutation groups -- often arising as automorphism groups of first order structures.

7. Homogeneous structures, in the sense of Fraisse. There are connections to permutation groups and combinatorics, and more recent connections to Ramsey theory, topological dynamics, and constraint satisfaction.

### Useful links

MALOA Initial Training Network

Personal Home Page

British Logic Colloquium

Leeds Logic Group

## Postgraduate students

Andres Aranda Lopez (2009)

Ricardo Bello Aguirre (2012)

David Bradley-Williams (2009)

Erick Garcia Ramirez (2013)

Daoud Siniora (2013)

Daniel Wood (2012)

## Selected publications

D. Haskell, E. Hrushovski, H.D. Macpherson, `Stable domination and independence in algebraically closed valued fields', Lecture Notes in Logic, Cambridge University Press, 2008.

M. Aschenbrenner, A. Dolich, D. Haskell, H,D. Macpherson, S. Starchenko, `Vapnik-Chervonenkis density in some theories without the independence property, I', arXiv 1109.5438.

M.W. Liebeck, H.D. Macpherson, K. Tent, `Primitive permutation groups of bounded orbital diameter', Proc. London Math. Soc. 100 (2010), 216--248.

R. Elwes, E. Jaligot, H.D. Macpherson, M.J. Ryten, `Groups in supersimple and pseudofinite theories', Proc. London Math. Soc. (3) 103 (2011), 1049-1082.

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