Date: Friday 2 March 2012, 4:30pm Location: Hempfield High School, Room 213 Speaker: Michael McCooey, Franklin & Marshall College Title: Orientability of fixed-point sets of group actions on four-manifolds Abstract. When a cyclic group acts on a closed four-manifold, preserving orientation, its fixed-point set is a collection of surfaces and isolated points. Usually the surfaces are orientable---but not always. We review what is known about necessary conditions for orientability, and construct some explicit examples to develop a feel for the subject. If instead the group in question is Z_2 x Z_2 (a case of particular interest to me), then the surfaces in the singular set come equipped themselves with some additional symmetry. We examine the consequences of this symmetry and pose a key question. This will be a user-friendly talk, leading up to a discussion of work in progress.