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Notice

AISB opportunities Bulletin Item

PhD student position on "Homogeneous structures", Leeds (U.K.)

http://www.findaphd.com/search/showproject.asp?projectid=22740&searchtype=n&page=1
Contact:

Homogeneous structures, homomorphism-homogeneity and automorphism groups

As part of an EPSRC grant at the University of Leeds with the title above, there will be a fully funded PhD studentship, and we seek suitably qualified candidates to begin their PhD in the autumn of 2009.


The PhD student appointed will be jointly supervised by Professors Macpherson and Truss, and will work on an aspect of the EPSRC research grant.  He or she will interact not only with the two investigators, but also with the postdoctoral research assistant, Dr Deborah Lockett. There will be regular meetings between the RA, the PhD student, and the investigators, and other interested research students, and probably a seminar with this group. We plan to hold a short meeting in Leeds on homogeneous structures.

The project concerns aspects of homogeneous structures. A countable structure is said to be 'homogeneous' if any isomorphism between finite substructures extends to an automorphism. The initial theory of homogeneous structures was developed as part of model theory. One of the key achievements was a classification by Cherlin (1998), of the homogeneous digraphs. The class of examples has great complexity but the description is clean and beautiful. However, the classification sheds little light on what homogeneous (even binary) structures look like in general.

The very general framework of homogeneity means that the subject touches many parts of mathematics, such as model theory, connections of finite model theory with computer science, group theory, descriptive set theory, and, in particular, combinatorics. Much of this has developed since Cherlin's memoir. For example, there is now wide interest in homogeneous metric spaces, in connections with structural Ramsey theory in combinatorics, and with topological dynamics. It has become urgent to revisit classification in homogeneous structures, to identify how far it can reasonably be taken, and whether, if one requires less than full classification, meaningful descriptions remain.

This is a project in combinatorics, but it has strong connections with model theory, group theory, and theoretical computer science. Candidates with interests in any or all of these areas may apply.

The studentship is advertised on http://www.findaphd.com/search/showproject.asp?projectid=22740&searchtype=n&page=1 and anyone interested is encouraged to contact one or both of the investigators on pmtjkt@leeds.ac.uk or pmthdm@leeds.ac.uk.