# Southampton, in the middle distance of my heart

I’m back today from a week’s holiday visiting old friends and colleagues in Southampton, where I spent the days haunting the maths department, helping myself to coffee and leaving behind the occasional half-pack of hobnobs. I’m on good enough terms with most of the pure group for them to have registered my absence over the last two years, but a fair few other people who I only know by sight gave me odd confused looks, as though they’d seen a dead man. Which, in a sense, I am. Besides hanging around in the coffee room, I had a nose around the research students’ office and was pleased to see that most of the crap I stuck on the door and on the wall above my old desk is still there, and indeed so are the strata of crap put there by still older students, now long-gone. But a good number of the current students overlapped with me; I am not yet become a name.

Aside from the one day’s worth of actual-job work that I smeared out over the whole week, I spent most of the time playing the part of a responsibility-less academic, like an Emeritus Professor but without the prior lifetime of acheivement. My PhD supervisor and I talked over some unfinished problems and new directions from my thesis, and worked through some related results by a student in Warwick. We didn’t prove anything new, but by the end of the week the maths part of my brain felt alive again and we came up with some quite ambitious plans for research threads to follow. I’m unsure if I’ll be able to sustain the interest once I go back to work but for now I’m optimistic.

In the first half of the week the department held a conference for Peter Kropholler’s 60th birthday, so I went to some of the talks for that. Nikolay Nikolov and Martin Bridson’s (both U. Oxford) talks were particularly enjoyable for me. Nikolay talked about the following theorem:

If G$G$ is an infinite compact group, then the set of conjugacy classes in G$G$ has cardinality \ge 2^{\aleph_0}$\ge 2^{\aleph_0}$.

The proof he gave was very impressive, one of those proofs that makes use of any and every tool available to get the job done, which I usually take to be characteristic of the best maths. Martin’s results—about the numbers of generators and relations necessary to present the Sidbi double of a group—were less quotable but similarly interesting. As an old friend of Peter Kropholler’s, Martin also had plenty of kind and funny remarks to make:

“Peter convinced me that algebra is worthwhile and that it’s something it’s possible to have intuition for. I don’t have the intuition, but Peter makes algebra sing”.

I also had a lot of fun just re-living what used to be my day-to-day maths department activities: wandering into the other student office and getting involved in a collaborative attempt to prove a lemma one student needed (it was false); going to the pure group colloquium and asking naive questions about coarse geometry; stealing stationery; baguette and a packet of monster munch from the student shop for lunch. I managed some of my other regular activities too: on Wednesday afternoon I took the train to Winchester and ran back to Southampton on the footpath route along the river Itchen, then got drunk on a school night with Joe “Joe Tait” Tait. I didn’t get to go to either of my favourite Southampton pubs though (the Butcher’s Hook and the Guide Dog). Next time.

This morning I got up early so I could do the parkrun1 before coming home. As I walked to the station from the Common through Southampton’s gorgeous cemetery (home to hundreds of Titanic victims), I reflected a little on my stay. I don’t know why, but I expected an extreme of feeling, either a deep love for the city and my time here and regret for leaving, or utter alienation from this place I lived for 8 years. In the end I had a nice week enjoying warm memories of a previous time. The regret I might feel that that time has now passed was tempered by the pleasure of discovering that it’s a past I am still able to visit, for a little while.

1. 18:07—new 5km personal best, thank you very much. ↩︎

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