Studies of complex spaces

Associate Professor Elizabeth Wulcan will receive funding from the Knut and Alice Wallenberg Foundation to recruit an international researcher for a postdoctoral position at the Department of Mathematical Science, Chalmers University of Technology and University of Gothenburg, Sweden.

The focus of the project is a study of complex spaces and their geometry. Geometry in the plane or in space is a classical branch of mathematics, dating back to ancient Greece. In the 19th century mathematicians became interested in geometry on curved surfaces such as a sphere or a torus (the surface of a donut). Manifolds are geometric objects that generalize such surfaces.

Complex manifolds are analogues of real manifolds, where the real coordinates of each point in space are replaced by complex ones. Complex numbers are an extension of the concept of real numbers, in which a square root of minus one exists. If we allow a complex manifold to have sharp edges or to cut itself it is called complex space.

While the geometry of complex manifolds is well understood, many questions about complex spaces remain open. Given a manifold there are ways of measuring the volume (or the area if the manifold is two-dimensions) of parts of it. Much of the geometry of the manifold is encoded in the set of possible ways of measuring volume. The research team will study different ways of measuring volume on a complex space, and by that hopefully contribute to obtain a more complete picture of the geometry of complex spaces.

Photo: Chalmers University of Technology