Alexandra Seceleanu (University of Nebraska)Title:  Principal symmetric idealsAbstract:  A ubiquitous theme in mathematics is that general members in a family of mathematical objects have nice properties. Several examples will be given to illustrate this principle, with emphasis on families of graded algebras and their homological properties. We will eventually focus on the family of principal symmetric ideals, that is, ideals generated by the orbit of a homogeneous polynomial under the action of the symmetric group. In joint work with Megumi Harada and Liana Sega we determine the minimal free resolutions for a general member of this family, as well as other notable properties it satisfies.