Proper Group Actions in Complex Geometry

We study the symmetries of geometric objects called manifolds. Manifolds are used to model curved spaces; for example, in modern physics the universe is represented as a manifold. Symmetries are combined in groups, and the way in which a group of symmetries moves points within a manifold is called the action of the group. We propose a novel study of an important class of actions, so-called proper actions. Such actions often arise in many areas of modern mathematics and physics. They are central to a variety of mathematical constructions and critical for understanding the universe through currently employed physics models.