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.