PhD studentship available: toposes and quantum theory

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

Dear categories list,

I have received EPSRC funding for a project with a PhD studentship
attached. If you know of suitably qualified students who might be
interested, I would be very please to hear from them. Study would be
in the School of Computer Science at Birmingham University, UK, and
the preferred start date is October 2009.

The project is "Applications of geometric logic to topos approaches
to quantum physics".

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

Regards,

Steve Vickers.