Post-doc position at Birmingham: toposes and quantum theory

[Steve Vickers <s.j.vickers@cs.bham.ac.uk>]

Research project: "Applications of geometric logic to topos approaches
to quantum physics".

[I have already announced a PhD studentship on this project, but a 3 yr
post-doc position has now come available.]

I have received EPSRC funding for a 3-year project with a post-doctoral
research position and PhD studentship attached, to be conducted in the
School of Computer Science in the University of Birmingham, UK, and to
start between now and October. I would be very pleased to receive
applications.

The essential area of expertise for the post-doc is constructive
reasoning (with toposes and point-free topology), but the researcher
will also need to have or acquire some familiarity with quantum theory.

The funding allows for appointment at a high salary grade for a suitably
qualified and experienced researcher.

The "topos approaches" referred to are those of Isham and Doering (at
Imperial) and Heunen, Landsman and Spitters (at Nijmegen). By working
internally in suitable toposes, they are able to find (commutative)
Gelfand-Naimark spectra for systems that, externally, are non-
commutative. The hope is that this might lead to a style of reasoning
about quantum systems that, while logically non-classical, is
physically classical.

My project will look at trying to keep the intuitionistic, topos-
valid, internal reasoning within its geometric part. Insofar as this
is possible (and there is mounting evidence that substantial amounts
of practical mathematics can be done this way), it enables a language
of points, stalks, fibres and bundles for the point-free topology
involved. It is hoped that this will allow the topos approach to be
conducted in terms that are more conceptually transparent (in
particular to physicists), but also make it technically palatable to
move from the present presheaf toposes to sheaf toposes. Initial work
will focus on the geometric content of the Banaschewski/Mulvey
account of Gelfand-Naimark duality.

Further information can be found on my web site, at

   http://www.cs.bham.ac.uk/~sjv/geophysics.php#phd

I can also supply a more detailed project description on request.

Steve Vickers.