Title: Associated Graded Rings and Connected Sums,
Abstract: In 2012, Ananthnarayan, Avramov and Moore gave a new construction of
Gorenstein rings from two Gorenstein local rings, called their connected sum.
In this article, we investigate conditions on the associated graded ring of a
Gorenstein Artin local ring Q, which force it to be a connected sum over its
residue field. In particular, we recover some results regarding short, and
stretched, Gorenstein Artin rings. Finally, using these decompositions, we
obtain results about the rationality of the Poincare series of Q.