The n-Category Café

What Happened At The Magnitude Workshop

Posted by Tom Leinster

A week ago we had a short workshop on magnitude at the University of Edinburgh, organized by Heiko Gimperlein, Magnus Goffeng and me. If that sounds familiar to you, it might be because I advertised it here before. The slides from the talks are now on the website. You can also see a list of open problems.

Anyway, it was a great meeting, focused on the magnitude of metric spaces (as opposed to enriched categories more generally), and roughly evenly split between the analytic and homological aspects of magnitude. It included talks from our own Simon Willerton and Mike Shulman, as well as other experts in a wide variety of different fields (as the official name of the workshop suggests: “Magnitude 2019: Analysis, Category Theory, Applications”). And Emily Roff, who’s doing a PhD with me, spoke about our work on the maximum diversity of a compact metric space.

Heiko and Magnus also invited some experts in the theory of capacity to help us out, knowing that this is something highly relevant to magnitude — even though it now seems that the kinds of questions about capacity that we’re asking do not yet have answers. I was particularly happy to see people from the algebraic side taking part in discussions on primarily analytic questions, and vice versa.

The talks were arranged so that each day started with some introductory stuff (schedule here), before going into more depth. So if you’re curious to find out more and read some of the talk slides, that’s where you might want to start.