Abstracts and Available Slides
Lecture 1, Cohomologically noetherian rings.
Abstract: The use of cohomological support varieties has produced novel
insight into the representation theory of various classes of
rings. Proofs of the basic properties of support varieties often
depend on specific constructions and are highly context-specific, but
invariably require some finiteness conditions on Yoneda
products structures. In the talk, based on joint work with
Srikanth Iyengar, the nature of such conditions will be discussed, and
it will be shown that they impose structural restrictions on the ring.
Lecture 2, Some applications of stable cohomology.
Abstract: Pierre Vogel defined a Z-graded multiplicative cohomology
theory for pairs of modules over associative rings, and showed that it
naturally contains Tate's cohomology theory of finite groups. I
will describe applications of algebra and module structures defined by
these functors to familiarly sounding questions about commutative
rings; the relevant results come from collaborations with Luigi
Ferraro, Srikanth Iyengar, and Oana Veliche. One of the goals is
to draw attention to this interesting, but still poorly understood
theory.