2022 Workshop on Polynomial Functors
This year, Topos sponsored a second workshop on polynomial functors. It consisted of 20 talks, spread out over five days (all of which have been recorded and can be found on our YouTube channel) Like last year, the organizers were myself and my friend and colleague Joachim Kock. Two things made this event different from that of last year.
This year, Topos sponsored a second workshop on polynomial functors. It consisted of 20 talks, spread out over five days (all of which have been recorded and can be found on our YouTube channel) Like last year, the organizers were myself and my friend and colleague Joachim Kock.
Two things made this event different from that of last year. First, it was very early in the morning for us Berkeley folks, starting at 7am and going until 11. Getting up before 6 and staying attached to the screen for four hours straight was not easy, but the talks were very much worth it!
The second thing that made this event different was that we included talks on “the other kind of polynomial functor”, which was actually the chronologically-first kind of polynomial functor, namely that of Eilenberg and Mac Lane (we referred to these as Eilenberg-Maclane polynomials and to the kind Joachim and I are more acquainted with as bundle or (I\leftarrow E\to B\to J)-style polynomials). We had three hours of tutorials on these, provided by Christine Vespa, as well as a number of other talks that related them to Goodwillie calculus, and other notions in algebraic topology and related fields. In particular, Elden Elmanto explained how one can apply a suitable cohomology theory to an (I\leftarrow E\to B\to J)-style polynomial and get an Eilenberg-Maclane style polynomial.
Similarly to last year, the talks on (I\leftarrow E\to B\to J)-style polynomials were quite diverse. We heard about type theory, including a two-hour tutorial by Steve Awodey, infinity-category theory, database theory, programming language theory, and many other themes, all written in the language of (I\leftarrow E\to B\to J)-style polynomials.
All in all, it was a great workshop. Many participants took the time to write to say they learned a lot, and I certainly did too. Brandon and I (the two speakers from Topos Institute) have begun talking with Todd Trimble about his talk, in which he explained how to view functors internally to the polynomial ecosystem. So at least for us, the workshop had a direct impact on our research. Hopefully, with the videos and slides online, the workshop will help people from a variety of backgrounds to see the value and fun, and the depth and breadth, of polynomial functors.