This grant supports a mathematical research institute during the summer of 1996. This institute will be the forty-third in a series planned with the purpose of bringing together a group of mathematics interested in a particular field of mathematical research. Emphasis is placed on instruction at a very high level with seminars and lectures by distinguished mathematicians in related fields, to promote interaction between participants while broadening their mathematical perspectives. "Cohomology representations and actions of finite groups" has been selected as the topic of the 1996 Summer Research Institute by the 1994 AMS Committee on Summer Institutes and Special Symposia. The 1996 Institute will be held in San Diego, California. It is expected to be held during a three-week period in July/August, 1996.