Support varieties and the Hochschild cohomology ring modulo nilpotence
This paper is based on my talks given at the '41st Symposium on Ring The- ory and Representation Theory' held at Shizuoka University, Japan, 5-7 September 2008. It begins with a brief introduction to the use of Hochschild cohomology in developing the theory of support varieties of (50) for a module over an artin algebra. I then describe the current status of research concerning the structure of the Hochschild cohomology ring modulo nilpotence.