These are pictures of the fjord taken from my office window. As well as being a fantastic view it also varies considerably from day to day. The weather changes quite quickly in Trondheim and the predominant direction is from the fjord. So one can often see what weather is coming.

To misquote John Baez, I don't take a new picture every day, but when I do, it is always i dag.

Actually, it's usually i kveld as I'm currently taking these pictures using a camera phone and my work machine won't talk to my phone as it's too posh (it will only talk to devices with the right connections) so I have to process the pictures at home before uploading them. That also explains why they aren't great quality.

Clicking on a picture should take you to a bigger version.

Older Pictures

We consider the problem of defining the structure of a smooth manifold on the various spaces of piecewise-smooth loops in a smooth finite dimensional manifold. We succeed for a particular type of piecewise-smooth loops.

We also examine the action of the diffeomorphism group of the circle. It is not a useful action on the manifold that we define. We consider how one might fix this problem and conclude that it can only be done by completing to the space of loops of bounded variation.

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This course studies the central ideas of functional analysis, focussing primarily on normed vector spaces.

Highlights include:

• The Hahn-Banach theorem (in various guises)
• The open mapping and closed graph theorems
• The Banach-Steinhaus theorem
• Dual spaces
• Weak convergence
• Banach-Alaoglus theorem
• Spectral theory for self-adjoint operators

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Algebraic Topology Special Session, BMC 2007

Infinite dimensional Riemannian manifolds have traditionally been divided into two types: strong and weak. One can generalise many of the standard constructions of Riemannian geometry to strong Riemannian manifolds but not to weak ones. In this talk I shall examine some of the basic results of Riemannian geometry in order to refine this classification. The purpose is to show that some constructions can be generalised to certain weak Riemannian manifolds. I shall conclude by describing which level of structure is available for the free loop space of a finite dimensional manifold and by explaining how this can be used in applications.

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This is my current curriculum vitae. It contains details of my education and employment since 1998, my publications, an overview of my teaching experience, a list of talks that I have given, and other miscellaneous information that may be useful.

In PDF or PostScript.

Some things that I keep having to look up about the Z-shell.

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• MathSciNet
• arXiv