The Well-Covered Space of Finite Geometries
Students in this group will study which of the possible approaches to define the well-covered dimension of a point-line configuration is the one that is most "useful". They will do this by finding the well-covered space for several standard geometric objects, such as projective planes/spaces, generalized polygons, and important subsets of them like ovals, ovoids, quadrics, varieties, etc.
The concept of well-covered dimension has been only used for graphs until now, and so our ultimate objective will be to create a theory for linear spaces, and other discrete geometric objects, that are not graphs.
An ideal member of this research group should have completed a proof class, a linear algebra class and, hopefully, a combinatorics and/or geometry class. Being enrolled in or have completed a graph theory and an abstract algebra course would be a plus.