Fatemeh Mohammadi: Weakly Polymatroidal Ideals

Abstract

In this talk weakly polymatroidal ideals will be defined. These ideals have linear quotients and so they are componentwise linear, which enables us to study powers of the ideals associated to graphs. First we see that in the squarefree case these ideals are related to vertex decomposable simplicial complexes. Then as an application we study powers of the vertex cover ideals of graphs, the case Cohen-Macaulay bipartite graphs and chordal graphs.