Professor in mathematics
In differential geometry, mathematical analysis is used to study geometric objects such as curves, surfaces and high-dimensional spaces, known as manifolds.
Mattias Dahl's research is concerned with differential geometry with applications in areas such as general relativity. A central theme of this research is the study of the connection between a manifold's geometric properties, such as distance and curvature, and solutions to partial differential equations for the space, which can be regarded as describing physical phenomena in the space. For example, Dahl has studies the so-called Dirac operator and its link to metrics with positive scalar curvature. In relativity, the research has been concerned with the geometry of initial data for Einstein's equations, corresponding to the universe at a single point in time. Dahl has also studied the concept of total mass in relativity and what is known as the Penrose difference which gives a lower limit to the total mass in terms of area of the event horizon.
Differential geometry is a field with many important applications. The goal of continuing research is to provide a deeper understanding of the links between geometry, topology and the analysis of manifolds.