
MathematicsPhD Thesis
In my PhD thesis I applied algebraic topology to problems that arise in geometry,
in particular problems involving closed geodesics. The topic of closed geodesics
on manifolds is a classical one, initiated by the likes of Morse and Lusternik
and Schnirelman who were interested in proving the existence of closed geodesics.
Another interesting problem is to study the geometry of manifolds all of whose
geodesics are closed. I worked on a conjecture by Marcel Berger, which states
that on a simply connected manifold all of whose geodesics are closed, the
geodesics all have the same least period. The assumption that the manifold is
simply connected is necessary, since for lens spaces with the standard metric,
all geodesics are closed, but not of the same least period.
Masters Thesis and Bachelor Project
You can download my Master of Science thesis about topologigal
properties of positively curved manifolds
here: ps, pdf.
NotesDuring the Spring 2010 I taught the course Introduction to Geometry. I wrote lecture notes for the course. In the notes, I develop the theory of conformal maps of the Riemann sphere. You can download the notes here. From September 2002 to June 2004 I was responsible for organizing
IMF's high school visiting programme. We gave lectures and organized
problem sessions for high school students. Our main aim was to get
gifted students interested in mathematics by giving talks about
advanced mathematical topics. You can see the webpage (in
Danish) "Besøgsservice".
Kurver i planen og rummet, ps, pdf.
Emil Hedevang Lohse, Erik Olsen and I have typed some lecture notes by
Johan Dupont on curvature and characteristic classes in LaTeX. You can
download the notes here: 
Last updated August 9th 2010.