Face Numbers of Cohen-Macaulay ComplexesAlgebra & Discrete Mathematics
|Speaker:||Jonathan Browder, University of Washington|
|Start time:||Fri, Nov 18 2011, 2:10PM|
One of the most fundamental invariants of a simplicial complex is its f-vector, which lists the number of faces the complex has in each dimension. One of the central challenges of geometric combinatorics is that of characterizing the set of f-vectors for interesting classes of complexes. A characterization of the f-vectors of Cohen-Macaulay complexes was given by Stanley; this result was refined to a characterization of the f-vectors of a-balanced Cohen-Macaulay complexes (Bjorner, Frankl, and Stanley) and a later to a characterization of the f-vectors of Cohen-Macaulay subcomplexes of joins of boundaries of simplices (B., Novik). This talk will present a common generalization of these latter two results (B., Novik), and explore some of the tools used.