Old and recent work with Maurice

Summary

I met Maurice in 1970 in Urbana, Illinois, where I was a graduate student of Robert Fossum. Maurice came to Urbana to work on representation theory. He gave an advanced course, where he usually lectured, with great enthusiasm, on what he had proved since the previous session. I saw something like this for the first time, and I found the mathematics, and Maurice's approach to it, very exciting. I had a fellowship from the Norwegian Research Council, which also could support me beyond my Ph.D. in 1971, and I wanted to go to Brandeis to work with Maurice. When I finally had the courage to ask him if this would be possible, he said that he had been thinking about the same thing, but he was not interested if I did not have the courage and initiative to ask. This was the start of a collaboration which lasted until Maurice's death, and which produced about 40 papers, some with additional coauthors. Maurice viewed the semester in Urbana as the start of his work on representation theory, as indicated by what he wrote to me:

(March 22, 74) It was really nice being back in Urbana, the place where all of this mathematics started.

I shall here give a survey of some of the main parts of our joint work, in an expanded version of my lecture at the Maurice Auslander Memorial Conference. The organization is according to topics, usually in the order in which the work started. No attempt is made to review the contributions of others on these topics, and the list of references is restricted to cover my work with Maurice.