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The end (or not?) | Peter Cameron's Blog
Rosemary and I have been in St Andrews for nearly twelve years, on temporary contracts. The current contract expires at the end of February 2025, and there is no money to renew it. So we will technically be retiring (or being made redundant) on that date. However, we will not immediately disappear, and it seems…
Simplicial complexes on groups | Peter Cameron's Blog
At the recent UMI/AMS joint meeting in Palermo, I had some brief discussions with somebody about this topic. But I didn't get contact details. If it is you, and you happen to be reading this, please get in touch! I have been thinking about this, and there are some interesting things to say and some…
New BCC website | Peter Cameron's Blog
The British Combinatorial Committee has a new website: www.britishcombinatorics.org.uk/ Take a look, and pass on any comments! My personal thanks to Julia Wolf. The WordPress site I maintained for several years will now be decommissioned. And on the subject of announcements, the next British Combinatorial Conference will be in Cardiff, 6-10 July 2026.
Two conferences, two mysteries | Peter Cameron's Blog
Two conferences in recent days. Time permitting, I would say more about each. I just want to point to two mysteries and some synergy. Last week I was at the British Mathematical Colloquium in Manchester. The last plenary speaker at the first was Nina Snaith, who talked about one of the most striking recent mysteries,…
Dominic Welsh memorial service | Peter Cameron's Blog
To Oxford last Saturday for the memorial service for Dominic Welsh. I wrote about Dominic here; the picture was taken at Geoff Whittle's conference in Wellington in December 2015, if my memory serves. Many people's lives were touched by Dominic, and it was good to see so many able to make it for the service.…
My first doctoral student | Peter Cameron's Blog
One of the hardest things for a supervisor of a new doctoral student is to choose a research topic. It should be one which is not trivially easy or impossibly difficult. But of course it is impossible to say in advance whether a problem will fall into one of these categories. It is especially difficult…
A talk on discrete mathematics | Peter Cameron's Blog
The Academy for Discrete Mathematics and Applications is an Indian organisation founded in 2005 to foster and support interest in discrete mathematics. The current president, Ambat Vijayakumar, has started up a Colloquium Lecture seres, and honoured me by asking me to give the first lecture. I decided that, rather than up-to-the-minute new research, a more…
British Combinatorial Conference | Peter Cameron's Blog
The British Combinatorial Conference returns to Queen Mary Univesity of London in the first week of July. The web page is here. Last time when the conference was there, and I was one of the organisers, the insttution was called "Queen Mary and Westfield College". We had 319 delegates, a record which has never been…
Graphs and groups, designs and dynamics | Peter Cameron's Blog
Four and a half year ago there was a conference and summer school on the four topics of the title (part of the G2 series of conferences, whose hiistory you can read here) at the Three Gorges Mathematics Center in Yichang, China. Now a book containing the notes from four lecture courses on the four…
A talk by Gareth Jones | Peter Cameron's Blog
Today I attended (remotely) a nice talk by Gareth Jones in the Ural Workshop on Group Theory and Combinatorics, about prime powers in permutation group theory and polynomials taking prime values in number theory. I will give just one example result from the first part. For a prime p, a p-complement in a group G…
Ischia group theory conference 2024 | Peter Cameron's Blog
The island of Ischia, about a 45-minute hydrofoil ride from Napoli, is rich in history. The museum has a Homeric drinking cup with an inscription in ancient Greek from the 8th century BCE. At the other end of history, the British composer Sir William Walton and his Argentine wife Susana bought a desolate hilltop producing…
West Virginia University | Peter Cameron's Blog
Anthony Hilton, my former colleague at Queen Mary, spent some time as an Eberly Professor at West Virginia University. Now he has passed on to me the news that the University has decided to close down Pure Mathematics research and put the money into "computer related activities", whatever that means. One of the last mathematicians…
Cauchy numbers: job done | Peter Cameron's Blog
After recruiting Scott Harper to the team, we have finished the job of determining all the Cauchy numbers (these are the positive integers n for which there exists a finite list F of finite groups so that a finite group has order divisible by n if and only if some member of F is embeddable…
Anatoly Vershik | Peter Cameron's Blog
Anatoly Vershik died the day before yesterday. As I have told here, he was the person who told me about the Urysohn space. I had given a talk at the ECM in Barcelona on the countable random graph, and after it he approached me and asked "Do you know about the Urysohn space?" We wrote…
Richard Parker | Peter Cameron's Blog
Richard Parker died last month. Now only two of the authors of the ATLAS of finite groups remain, the two Robs. I knew Richard, but perhaps not well enough to write anything appropriate as a tribute. But I recommend you take a look at Rob Wilson's account on his blog.
More on Cauchy numbers | Peter Cameron's Blog
Following on from the earlier post, the new version of the paper has just gone on the arXiv: 2311.15652 (version 2). If we say that n is a Cauchy number if there is a finite set F of finite groups, all with orders divisible by n, such that every group with order divisible by n…
Cauchy’s theorem for the prime 6 | Peter Cameron's Blog
Before you think I have gone totally crackers: Cauchy's theorem says that a finite group whose order is divisible by a prime number p contains a subgroup which is cyclic of order p. My co-authors and I have proved some similar results, of which the one referred to in the title is the following: A…
Simon Norton lecture | Peter Cameron's Blog
I have been honoured by an invitation to give the inaugural Simon Norton lecture at the London Institute for Mathematical Sciences on 12 February. The webpage is here. Of course there are other people who knew Simon better than I did. Nevertheless, I think I have something to say. It was a paper of mine,…
New Year | Peter Cameron's Blog
The youth could not help breaking a rule of courtesy towards this heavily burdened and yet, as he felt, noble man by asking: "But tell me, I beseech you, why do you carry on such wars on your star? Who is to blame for them? Are you yourself in part responsible?" The King seemed angered…
Programming and typesetting | Peter Cameron's Blog
Is computer typesetting a kind of programming? One of the pioneers, Donald Knuth, clearly thought so. In The TeXBook, he gives TeX code for computing and typesetting the first thirty primes; apart from anything else, this demonstrates that TeX has the capacity to act as an all-purpose program. But there is a rather significant difference.…
Dominic Welsh | Peter Cameron's Blog
Dominic Welsh died late last week. Dominic and I were tutors at Merton College, Oxford for nearly eleven years. I was the pure maths tutor and he was the applied maths tutor. But there was no other Oxford college where the mathematical interests of the pure and applied maths tutors were closer. College lunches are…
Covers of groups | Peter Cameron's Blog
Here is the second of these discussions of elementary problems on finite groups with unexpected ramifications. This topic was suggested to me by Hamid Reza Dorbidi form Jiroft, Iran. Let F be a finite set of finite groups. A finite group G is a cover of F if every group in F is isomorphic to…
“Words that tear and strange rhymes” | Peter Cameron's Blog
In his youth, Paul Simon thought of himself as a poet: On a tour of one-night stands My suitcase and guitar in hand And every stop is neatly planned For a poet and a one-man band He thought about his craft: My thoughts are scattered and they're cloudy They have no borders, no boundaries They…
Coherent permutation groups | Peter Cameron's Blog
This post, in a sense, follows on from the previous one, though I won't explain the connection just yet. Here is another property of permutation groups which occurred to me last night. I have no idea yet whether it is worth anything at all, but I am open to ideas. Let G be a group…
EPPA numbers of graphs | Peter Cameron's Blog
A paper with this title has just gone on the arXiv, 2311.07995. The random graph, discussed at length here earlier, has the property of homogeneity: any isomorphism between finite subgraphs can be extended to an automorphism of the whole graph. Now unfortunately there are very few finite homogeneous graphs. They were all found by Tony…
Connections | Peter Cameron's Blog
A small story about how these things work. This is a paper with six authors, which has just been accepted for publication in the diamond journal Combinatorial Theory. James East and three other semigroupists, Des FitzGerald (my classmate at the University of Queensland some time ago), James Mitchell (my colleague now in St Andrews), and…
Refereeing | Peter Cameron's Blog
Fairly recently I submitted a referee report to one of the big academic publishers. At the end of the process, it asked me whether I wanted it to tell ORCiD that I had submitted a referee report. Instinctively I said no. Later, I started wondering why. It seemed with hindsight that I had good reasons.…
Gary Seitz | Peter Cameron's Blog
News came that Gary Seitz died at the end of October. My one paper with Gary (also Cheryl Praeger and Jan Sazl) was the proof of Sims' conecture, stating that the order of the point stabiliser in a primitive group is bounded by any non-trivial subdegree. The proof uses the Classification of Finite Simple Groups;…
Scott Morrison | Peter Cameron's Blog
Last Friday, former Australian prime minister Scott Morrison did a question and answer session in St Andrews, hosted by Stephen Gethins of the International Relations department (and former SNP MP for north-east Fife). Rosemary and I went along; we were by some margin the oldest people there. I expected to disagree with him on various…
Ordering groups by element orders | Peter Cameron's Blog
Recently a couple of people have asked me questions, or suggested research topics, related to what appear to be elementary properties of finite groups, but on examination, show unexpected complexities. Part of the reason why group theory is such an endlessly fascinating topic. This one comes from Hiranya Kishore Dey in Bangalore, India. I hope…
A cautionary tale | Peter Cameron's Blog
This was just reported to me by a group theorist. He asked ChatGPT whether Aut(G) wr Sym(n) is a subgroup of Aut(G^n). It was honest enough to say that it didn't know (though it said it in a rather roundabout way). Then he asked whether equality holds when G is a finite simple group. This…
Some challenges on Latin squares | Peter Cameron's Blog
Following the combinatorial design challenges, here are three questions on Latin squares. A Latin square is an n×n matrix with entries from an alphabet of size n (typically the integers from 1 to n) such that each letter appears once in each row and once in each column. A transversal is a set of n…
Challenges in combinatorial design theory | Peter Cameron's Blog
Since WordPress changed their editor and it is no longer possible to write posts in HTML, I have to find a new solution to posting mathematics. What I have done this time is to put it on my web page on GitHub (https://cameroncounts.github.io/web/) and link it from here. On Thursday last week, Peter Keevash came…
Donald Keedwell | Peter Cameron's Blog
News came yesterday that Donald Keedwell has died. Donald Keedwell was the author (with J. Dénes) of a classic, Latin Squares and their Applications, first published in 1974 with a foreword by Paul Erdős, and still the best source of reference. In my work with Rosemary Bailey, Cheryl Praeger and Csaba Schneider, we used a…
Order of authors | Peter Cameron's Blog
The order in which the authors of an academic paper are listed is a perpetual source of trouble, partly since the approved order various between disciplines, so the contribution of authors of interdisciplinary papers is likely to be misunderstood. In some areas, authors are ordered by the relative importance of their contributions. This leads to…
New diamond journal | Peter Cameron's Blog
Welcome a new diamond open access journal, Innovations in Graph Theory, which has just been announced. Ross Kang asked me to spread the word, which I am very happy to do. The journal is based at the Mersenne Centre in Paris, and so is a stablemate of Algebraic Combinatorics. The webpage is https://igt.centre-mersenne.org/ . The…
Ian Macdonald | Peter Cameron's Blog
More sad news: Ian Macdonald has died. (To avoid confusion, this is the Ian Macdonald who introduced the Macdonald polynomials, not the one who taught me group theory.) My first exposure to the ideas of algebraic geometry came at Oxford, from the Mathematical Institute lecture notes called "Notes on Commutative Algebra" by Atiyah and Macdonald,…
Journals | Peter Cameron's Blog
The Internet and the World-Wide Web have brought us open-access journals. These appeal to bureaucrats because they want the results of publicly-funded research to be available to everyone, so we are now mandated to publish our work with open access, with various sanctions for not doing so. I have said many times that, of the…
Robbie Robertson | Peter Cameron's Blog
News this morning that Robbie Robertson has died. One of the great guitarists and songwriters of his era, he backed Bob Dylan, who described him as "the only mathematical guitar genius I've ever run into who doesn't offend my intestinal nervousness with his rearguard sound". I am not quite sure what that means. But for…
David Wales | Peter Cameron's Blog
We have lost another group theorist, David Wales. An email from Rebecca Waldecker gave a link, but WordPress is playing up and I can't share it. The link gives an account of his many contributions to group theory and algebraic combinatorics, especially his work on constructing and identfying sporadic simple groups including the Hall--Janko and…