# Differential Geometry

Geometry has always been a very important part of the mathematical culture, evoking both facination and curiosity. We have all dealt with the classical problems of the Greeks and are well aware of the fact that both modern algebra and analysis originate in the classical geometric problems.

Prof. **Sigmundur Gudmundsson** runs a research group in differential geometry with his students and postdocs. Information on the main research topics can be found at **Research Interests.**

Here you find the group's **Research Output**.

To present the latest developments in the field, the group annually organises the international **Differential Geometry Day **at Lund.

As a part of our standard curriculum we annually offer a course on **Gaussian Geometry** i.e. the elementary differential geometry of curves and surfaces in 3-dimensional Euclidean space. To this we annually offer a continuation on **Riemannian Geometry**. For PhD students we can offer a wide selection of higher level courses on the subject: Differentiable Manifolds, Comparison Theorems in Riemannian Geometry, Symmetric Spaces, Complex Manifolds, Morse Theory, Principal Fibre Bundles and Connections, Harmonic Maps, Loop Groups and Integrable Systems, etc.

The facinating picture above shows the famous Penrose singular foliation of the 3-sphere by tori and two circles after a stereographic projection into Euclidean 3-space. It was created by the GRAFMAT-group at the University of Cagliari.