[Turkmath:6539] PhD studentship at Leeds University (fwd)

[Ayse Berkman]

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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 at leeds.ac.uk<mailto:pmtjkt at leeds.ac.uk> or
pmthdm at leeds.ac.uk.