Date: 1 February 2013, 4:30pm Location: Hempfield High School, Room 213 Speaker: Samuel Kolins, Lebanon Valley College Title: Face-Vectors of Subdivisions of Manifolds Abstract. Start with a subdivision of a manifold into cells (for example a simplicial complex). A natural property to consider is the face-vector: the list of how many cells there are of each dimension. A major area of study is understanding the possible face-vectors for various underlying manifolds and different types of subdivisions. In this talk we will look at the progress that has been made on this question for two different types of subdivisions, simplicial complexes and simplicial posets, and two different manifolds, balls and spheres. Along the way, we will introduce the face ring, a beautiful and powerful tool that allows techniques from commutative algebra to be used to solve combinatorial problems.