Afshin Goodarzi: Possible h-triangles of Sequentially Cohen-Macaulay complexes

Motivated by several examples coming from subspace arrangement, Anders Björner and Michelle Wachs generalized the notion of shellability to the "non-pure" setting. They also defined the notion of h-triangle of a complex. The h-triangle is a finer invariant then the h-vector, in the sense that one can obtain the later from the former.  The notion of Sequentially Cohen-Macaulay (SCM) complexes were introduced by Stanley in order to provide an algebraic counterpart of the concept of (non-pure) shellability.  In this talk, I will present a numerical characterization of all possible h-triangles of SCM complexes. Further, some consequences of this characterization in commutative algebra will be discussed. (Based on a recent joint work with K. Adiprasito and A. Björner)