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.