Research Projects

PIs study the regularity and depth of powers of facet ideals I(∆) of a simplicial tree ∆. The first goal of this proposal is to prove that for a simplicial tree ∆ and s ≥ 1, reg(I(∆)^s) ≤ d(s-1)+reg(I(∆)), where d=max{|F|: F is a facet of ∆}. Another objective is to find the stabilization index Stab(I(∆)) and the constant, lim_{s→∞}depth(R/I(∆)^s) of I(∆) in terms of the combinatorial data associated with the simplicial tree ∆.