TITLE: Tate homology over associative rings



ABSTRACT: Tate homology and cohomology originated in the realm of

group algebras and evolved through a series of generalizations to the

setting of Iwanaga-Gorenstein rings. The cohomological theory has a

more far-reaching generalization to the setting of associative rings;

it is now called stable cohomology, and it agrees with Tate homology

over Iwanaga-Gorenstein rings.



On the homological side, the picture has remained opaque. In the

talk I will report on recent work---joint with Olgur Celikbas, Li Liang,

and Grep Piepmeyer---that clears it up a bit.