Study of Rees algebras and form rings

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What I want to do in my research is to study certain ring-structures (such as Buchsbaumness, Cohen-Macaulayness, or Gorensteinness) of Rees algebras associated to ideals in Noetherian local rings, from the view-point of the corresponding properties of their associated graded rings. In [G1] I gave a characterization for the Rees algebras associated to m-primary ideals of minimal multiplicity in Cohen-Macaulay local rings (A, m) to be Buchsbauxn rings, in terms of the corresponding property of the associated graded rings and the extended Rees algebras as well. As a byproduct of this research I constructed a counterexample to the negative a-invariant conjecture raised by Korb-Nakamura, concerning a question on the Cohen-Macaulayness in Rees algebras. Igave a lecture about the examples in the International Conference on Commutative Algebra in honor of David Buchsbaum (the third period, Genova) in Italy ([G2]). Also, K.Yarnagishi [Y] generalized the techniques in [G1], and gave a striking criterion for the associated graded rings of m-primary ideals in Buchsbaum local rings to be Buchsbaum, in terms of the Buchsbaum invariant. He gave a talk about this criterion at the International Conference on Commutative Algebra in honor of David Buchsbaum (the first period, Catania) in Italy, which I organized as one of the organizers. I am also interested in non-commutative algebra and performed ajoint research with Kenji Nishida. Someof the results will appear in [GN1, GN2].