Speaker: Branden Stone

Title: Super-Stretched and Graded Countable Cohen-Macaulay Type

Abstract: This work was motivated by a question of Huneke and Leuschke; let R be a complete local Cohen-Macaulay ring of countable Cohen-Macaulay type, and assume that R has an isolated singularity. Is R then necessarily of finite Cohen-Macaulay type? We show that such a ring is super-stretched. We also give a partial result to a the following folklore conjecture: A Gorenstein ring of countable Cohen-Macaulay type is a hypersurface. In particular, we show this conjecture is true in the one dimensional graded case.