- Jonathan Keelan is a new full-time research student starting in October 2011. Jonathan's topic is
Modelling of Embolic Stroke, and his lead supervisor is Jim Hague.
- Harry Kennard is a new full-time research student with lead supervisor Michael Wilkinson. Harry's topic is Dynamics in Turbulence, and he started on 1 August 2011.
- Penny Lynch
started as a part-time research student in October 2004, with
Andrew
Read (Edinburgh) as external co-supervisor. Her research is on the Mathematical Modelling
of Pathogen Life History Evolution Effects of Public and Animal Health Interventions.
- Manuela
Heuer started as a full-time EPSRC-funded research student
in October 2006. Her topic was
Combinatorial Properties of Sequences and Tilings.
Her co-supervisors were Andrey Umerski (internal) and
Michael
Baake (Bielefeld, Germany). Manuela completed successfully in 2010.
- John Urquhart was a part-time research student from 2007 until 2010. John's topic was Criteria for measuring the appearance and
transmission of DNA mutations in a human population, he was co-supervised by
Álvaro Faria (internal) and
Heather Cordell (Newcastle).
- William Stevens
was a part-time PhD student working on Artificial Life. He
started his PhD in January 2004 under my co-supervision (with
Nigel Mason).
William completed successfully in 2010.
- Svenja Glied is a
full-time research student at the University of Bielefeld,
Germany, supervised by Michael
Baake (Bielefeld). Svenja is a Visiting Research Student
at the Open University until end of April 2009.
- Miguel Tierz
was a full-time research student between February and June 2004, working on
Random Matrix Theory and Chern-Simons theory.
- Dr Tini
Garske, who had started her PhD project entitled
Models of biological evolution and statistical mechanics
in October 2001, obtained her degree in March 2005. After working at the London School of
Hygiene & Tropical Medicine, Tini is currently a Research Fellow at the Institute
for Mathematical Sciences at Imperial College, London.
- Dr
Przemyslaw Repetowicz, who is currently at Trinity College
(Dublin),
completed his PhD on
Theoretical
investigations of magnetic and
electronic properties of quasicrystals
at Chemnitz University of Technology in October 2000
(supervised jointly with
Michael Schreiber).
Interplay of mutation and selection in population genetics
Population genetics describes biological evolution in mathematical
terms. Methods of statistical mechanics can be employed to investigate
certain models of sequence evolution of DNA sequences, which can be
mapped onto classical or quantum spin systems. There is a close
collaboration to groups in Germany, both in mathematics and in biology.
One aspect of the work is the implementation of the DMRG (density matrix
renormalisation group) method that allows efficient numerical treatment
of finite systems of reasonable size.
Spectral properties of aperiodic Schrödinger operators
Aperiodically ordered quantum systems are of interest in the
theoretical description of quasicrystals, a particular kind of
ordered solid lacking the periodic structure of ordinary crystals.
Such systems exhibit rather unusual spectral properties, including
singular continuous spectra and multifractal eigenfunctions. The
work aims at unravelling the connection between spectral properties
on the one hand and quantum diffusion on the other hand, employing a
combination of analytical and numerical techniques.
Stastistical mechanics of aperiodically ordered and
disordered systems
The properties of a system at, or close to, a second-order phase
transition are assumed to be universal. Roughly, this means that they
do not depend on any particular details of the system. However,
aperiodic order or disorder, either in the coupling constants or
in the underlying discrete structure, may influence the critical
behaviour. The work comprises the investigation of the effects of
aperiodic order and disorder in classical and quantum spin models,
particularly the Ising model.
Any student who is interested to join me on one of the
above topics, or would like to know more about my research interests,
is cordially invited to contact
me!
