Seventy Years Using Fixed Points

domain theory
lambda calculus
type theory



Having first heard about theorems on fixed points as an undergraduate, uses for them came into my research on many subsequent occasions. The talk will review some personal history and give some suggestions for possible further applications.

When I saw last January that the International Conference Computer Science Logic (CSL 2023) would take place in Warsaw on 17 February 2023 with a satellite workshop Fixed Points in Computer Science (FICS 2023), I felt very sad to miss these events. But then it occurred to me I could perhaps send a video talk. I wrote the workshop organizers my offer, which they very kindly accepted. Now some months ago at the Topos Institute I had worked with the summer interns on many aspects fixed-point theories and collected lots of background bibliography. Also I had some good slides from a past conference. So I was able to edit things together to make some new slides I hoped to be appropriate for the workshop.

I then planned the speaking script for the talk, and — after getting some advice and doing some practice — I made a Zoom recording. My first! There were many glitches and the slide formatting was not so good. Fortunately our daughter, Monica, for her teaching and music recordings, has become an expert video editor. She did a great job in record time, so I was able to send the video and slide files to the workshop in good time. The program for the workshop can be found at A recording of the talk can be found on YouTube and a copy of the slides here.

Much of my motivation for doing this effort came from my long friendships and associations with Polish logicians and mathematicians — and many visits to Poland over the years. And some of that history I wanted to put into the talk. I was especially lucky while doing my preparation in tracking down the son of my first research collaborator, Jan Kalicki, who fortunately could supply a photo from the early 1950s. He is Jan H. Kalicki, a retired and a very distinguished professor of economics. He was only 5 years old when his father died in an automobile accident in 1953, and he was very touched to learn I could highlight his father’s memory in this way at the Warsaw meeting.

But, I am not wanting to dwell on the past, and there are many recent contributions to fixed-point theory, some of which I mention in the slides. Those references and the FICS workshop program indicate that the field is still very active.