London Algebra Colloquium

In two weeks’ time, the London Algebra Colloquium commences its sixty-second year, with a talk by Eamonn O’Brien (title to be announced), which will be number 1254.

There may be many mathematics seminars which have been running as long as this. But one remarkable feature of the LAC is that it has virtually complete records right from the start. On 25 October 1950, G. A. Dirac of King’s College gave the first colloquium talk, entitled “Graphs I”.

This shows a couple of ways in which the colloquium has changed. This was the first of a two-part talk, the second part being presented a fortnight later (the colloquium was fortnightly in the early days). I guess that the talks were partly expository, though there is no way of finding out. For example, colloquium 57, on 14 October 1954, was “An introduction to Burnside’s problem” by K. Gruenberg (Queen Mary College), followed three weeks later by G. Higman (Manchester) on “Burnside’s problem”. Later there were three talks by Dr C. Zeeman (Cambridge) on “Spectral sequences”, and three by Dr M. F. Atiyah (Cambridge) on “Characters and cohomology of finite groups”. This pattern became less common; but much more recently, number 1036, on 24 May 2001, was two talks by Viacheslav V. Nikulin (Liverpool) on “Borcherds’ proof of the Moonshine conjecture”.

Also, graphs were regarded as a part of algebra: no longer the “slums of topology”, but not yet a subject in their own right. Indeed, many people later known as graph theorists or combinatorialists spoke in the early days of the colloquium: R. Rado (King’s College), A. W. Ingleton (King’s College), P. Erdős (Aberdeen, and later University College), N. G. de Bruijn (Delft), C. A. B. Smith (University College), G. Szekeres (Adelaide), all spoke in the first 50 colloquia.

I already mentioned Karl Gruenberg. His first talk was Colloquium 46, on 26 November 1953, on “Residual properties of groups”; an astonishing fifty-three years later, his last, Colloquium 1141, was on 16 November 2006, on “The generation gap of free products”; in between, he spoke many times. This is not the last time his name occurs in the list: on 13 March 2008, Colloquium 1175 was a Karl Gruenberg memorial day, with talks by Bert Wehrfritz, Peter Kropholler, and Al Weiss.

Karl himself was one of the main reasons for the preservation of this extraordinary record. I don’t know where he had got them from, but he passed on to me a paper file with all speakers and titles up to that point. I transferred them to the Web (they are here, take a look), and with the help of Colloquium organisers since then, I have kept the records going.

My copy-typing is less than perfect, and there are certainly some misprints in the files! There are also (very) few gaps, and some inconsistencies (such as whether two talks on the same day count as one meeting of the Colloquium or two).

One innovation I have made is that, when a speaker provides an abstract, this is also kept on the web page. The first abstract in the collection is of number 1094, Rob Wilson’s talk “Finite groups with small automorphism groups” on 7 October 2004.

It is a matter of regret that no information other than name, title and date is available before this. I would very much like to know what some of those early talks covered (for example, number 10, “Inequalities associated with permutation groups” by R. Rado). Once I was emailed by a historian of mathematics asking what the contents of a particular talk had been, and had to reply that I had no idea. But in some cases it is easy to guess: for example, number 109, Dr J. A. Green (Manchester) on “Vertices of modules over a finite group”; number 173, by Professor D. R. Hughes (University of Michigan) on “t-designs”; or number 194, by Professor G. Higman (Oxford) on “The non-existence of certain generalized polygons”.

The London Algebra Colloquium, as its name says, was inter-collegiate. While most departmental seminars started at 4.30, the LAC always began at 4.45, to give people travelling from other colleges a bit longer to get there.

My first “proper” job was at Bedford College in 1974. I shared an office with Warren Dicks; he and I would set off on Thursday afternoons to walk to the Colloquium, in King’s or University College or wherever it happened to be that term.

The University of London has probably changed far more than the LAC in 61 years. The algebraists at King’s decided at a certain point that they were really number theorists, and started up their own seminar; Bedford, Westfield, Queen Elizabeth and Chelsea Colleges ceased to exist, being swallowed up by larger institutions; Imperial left the University (though continue to host the Colloquium in the spring semester); City University has, in some sense, joined, though they do not yet host the Colloquium. So at present it alternates between Queen Mary and Imperial.

The LAC records will outlast me. Sooner or later, someone else will take them over, and maybe make some changes. One day, every talk will be filmed and the videos will be available directly from the list. Who knows what else will change?