From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/144 Path: news.gmane.org!not-for-mail From: Steve Vickers Newsgroups: gmane.science.mathematics.categories Subject: PhD studentship available: toposes and quantum theory Date: Wed, 11 Mar 2009 16:43:43 +0000 Message-ID: Reply-To: Steve Vickers NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v753.1) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1236892357 30293 80.91.229.12 (12 Mar 2009 21:12:37 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 12 Mar 2009 21:12:37 +0000 (UTC) To: Categories list Original-X-From: categories@mta.ca Thu Mar 12 22:13:53 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1LhsDw-0005Fy-BZ for gsmc-categories@m.gmane.org; Thu, 12 Mar 2009 22:13:52 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LhrRa-0000YL-Lp for categories-list@mta.ca; Thu, 12 Mar 2009 17:23:54 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:144 Archived-At: 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.