I was privileged to be able to attend, to give its full title, the 53rd Southeastern International Conference on Combinatorics, Graph Theory and Computing, in Boca Raton, Florida. Does any other conference in the area have such a long and distinguished track record?

This year’s conference was a hybrid event, with roughly one-third of the participants on site (and who wouldn’t want to be in Florida at this time of year?) and the rest attending remotely from all over the world. Running a hybrid conference presents difficulties which don’t occur for either a conventional conference or a completely on-line meeting. The organisers have done a huge amount of work to ensure that everything would run smoothly: all remote speakers were given the opportunity to practise in advance.

Had things been otherwise, I would have loved to be there in person. But this was not possible, so they allowed me to attend remotely. Of course, if I had really been there, I would have had to make other arrangements for all my teaching; since I was still in St Andrews, I tried to have it both ways, using the five-hour time difference, so that I could do my teaching (mostly) in the morning and then spend afternoons virtually in Florida. Of course, had I been there, I would have been immersed in the conference, and attended many more talks than I actually managed.

I gave two talks, one on the geometry of diagonal groups, and the other on graphs on groups. The latter will be familiar from many recent posts here; the former is what I consider one of my best theorems ever, describing operands for diagonal groups as special semilattices of partitions (with Rosemary Bailey, Cheryl Praeger and Csaba Schneider, together with some further work and extensions involving also Michael Kinyon).

There was a problem in the second talk, when something froze up and the participants were left with my frozen image until I was able to leave and rejoin in Zoom, after which everything worked fine. Thanks to the organisers for enabling this so efficiently.

The conference was organised on a platform called Whova. It used Zoom as the main engine for presentations, but provided messaging facilities, virtual meeting rooms, and many other things including a leaderboard. (As I have explained in connection with MathOverflow, I don’t do mathematics in order to score points, so I spent very little time looking at the leaderboard! It reminds me a bit of a musical piece I heard once at the Royal Festival Hall in London. It was a “Competition for two orchestras and conductors”, where the conductors could choose what part of the score to play and points were awarded. Part of the problem was that we had not a clue what the points were awarded for. Many people walked out.)

In addition to the plenary talks, there was a special session on Matroids and Rigidity, with many speakers, including my colleague Louis Theran, my former colleague Bill Jackson, and my co-author Bob Connelly. This is now an active interdisciplinary area, and there were some exciting talks. Other speakers in parallel sessions included our recent visitor Mike Kagan (who spoke on our joint work on resistance distance and association schemes), former Queen Mary student Matt Ollis, and Aparna Lakshmanan S, one of the organisers of the research discussion on graphs and groups in Kochi.

That is great, continue the good work Sir, I would have loved to be there or follow the conference. I really missed.

Regarding the topic of your first talk: I must confess that while I did notice this paper when it went on the arXiv I have not found sufficient energy/focus to read in any depth. If I may be permitted one of those standard “ask something at the end of the seminar which is sensible but has no deep insight” questions: what is known about the standard semilattice-theoretic invariants of these diagonal semilattices, such as width, height or breadth, and how these might reflect properties of the group T?

I don’t think much is known about that. The height is equal to the number m. I do think that properties depending on the group are potentially the most interesting; this is why I banged on about chromatic number of the diagonal graph, as well as its connection to synchronization. But I hope there are nice answers to these questions.