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Trust in the Lord, and do good;

so you will dwell in the land, and enjoy security.

Take delight in the Lord,

and he will give you the desires of your heart. Psalm 37vv3-4

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I am a førsteamanuensis at the Department of Mathematics at the Norwegian University of Science and Technology, otherwise known as NTNU.
This website is divided into the following sections:

• Research. Details of my research and of my papers and preprints.
• Seminars. Details of those seminars that I have given where I have produced notes in a reasonable enough state for others to read.
• Professional. Information regarding my professional status such as my CV, a detailed research plan, and information about my teaching experience.
• Teaching. Information about my current teaching duties.
• HowDidIDoThat. Hints, Hacks, and Howtos for making computers work how I want them to and not the other way around.
• Links. Various links that I either use frequently or consider to be important.
• Fjord. Some pictures of the fjord from my office window.

On each index page you see the articles in that category plus the most recent articles from each of the subcategories. There are also Atom and RSS2.0 feeds for the various categories (but not for the individual articles). The menu on the left and the breadcrumbs at the top should help with navigation.

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 define the notion of a co-Riemannian structure and show how it can be used to define the Dirac operator on an appropriate infinite dimensional manifold. In particular, this approach works for the smooth loop space of a so-called string manifold.

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Linear problems occur throughout mathematics and its applications. This course will examine the mathematical tools needed to study such problems. The simplicity and elegance of these tools is part of what makes linearity such a desirable property. Indeed, many problems that are not inherently linear are often made linear as a first step in their analysis.

Problems that require only a finite number of pieces of information to specify them can be reduced to the study of matrices and coordinate vectors. However other problems, such as the evolution of a sound wave, require so-called infinite dimensional analysis. In this course we shall study both.

The topics that we shall cover include:

• Approximation and metric spaces
• Linear transformations and their characteristics
• Infinite dimensional linear spaces

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Being a mathematician requires a careful balance of two important character traits: tenacity and laziness. A mathematician will not let go of a problem until an answer has been found, but equally a mathematician would rather find an easy answer than a difficult one, even if finding the easy answer takes longer than the more direct one.

Laziness also means that mathematicians are extremely reluctant to give up a good theory. If a theorem was useful in one area, it is reasoned, it ought to be useful in others as well - even if there is no apparent connection between the two.

One of the most successful, certainly the most practical, areas of mathematics is calculus. And so mathematicians have spent hundreds of years pushing calculus into areas that it should never have been taken to so that now calculus appears in just about every area of mathematics, from number theory to discrete dynamics.

Differential topology is one of the milder outposts of calculus, yet even there one can encounter spaces that would make Isaac Newton's head spin. In some spaces, the back of your head is the front, and the middle of the top of the right hand side of the front is the back. Even Einstein would get lost here (though due to relativity, it would not be him that was lost but the universe around him would be lost).

In these spaces, it's wise to have a look first from a safe distance before venturing further in.

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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