Contents of this page
| August and September 2010 |
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I will be away for most of the next month. I should be reading email for at least part of the time. |
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I will be in my office on 26 and 27 August and will be back on 10 September. |
| Landscape document for Combinatorics |
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| I need your help to compile this document for the forthcoming International Review of UK mathematics. Please read this page and send any comments to me by mid-September. |
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"I count a lot of things that there's no need to count," Cameron said. "Just because that's the way I am. But I count all the things that need to be counted." Richard Brautigan, The Hawkline Monster: A Gothic Western, Picador, 1976. |
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Them as counts counts moren them as dont count Russell Hoban, Riddley Walker, Jonathan Cape, 1980. |
Contents of this page |
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Environment |
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I am a Professor of Mathematics, and Director of Pure Mathematics, in the School of Mathematical Sciences at Queen Mary, University of London. The street address, phone and fax numbers, and directions, are given below. A picture of the College is here.
For information about research in mathematics, see the School's research page; for details of postgraduate study see the postgraduate page.
I am interested in permutation groups, and the (finite or infinite) structures on which they can act (which may be designs, graphs, codes, geometries, etc.). Those countably infinite structures with the most symmetry are the ones which can be specified by first-order logical axioms; this is a general framework which includes many counting problems for types of finite structures. To get more detailed information, take a look at the abstracts of my recent and forthcoming papers, the problems which have appeared on this page, or my conjectures. Like the hero of Richard Brautigan's novel, I like to count things!
Some of my current interests are the connections between optimal designs and Laplace eigenvalues of multigraphs (I spoke about this at the British Combinatorial Conference in St Andrews last summer); homomorphisms and cores of symmetric graphs, which connect with automata theory and permutation groups; algebraic number theory properties of chromatic roots; orbit-counting versions of the Tutte and related polynomials; isometry groups of the Urysohn metric space; products of permutation groups; a 2-(14080,1444,148) design (constructed by Hunt and Rudvalis) admitting the Fischer group Fi22, and a 2-(1408,336,80) design (constructed by Praeger and me) admitting 212:(3M22.2); equivalence and typical properties of Latin squares; asymptotics of various counting problems (incidence matrices, 2-covers, etc.); and further properties of the random graph and related groups.
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| Combinatorics | Introduction to Algebra | Sets, Logic & Categories | Permutation Groups |
| Cambridge Univ. Press | Oxford University Press | Springer-Verlag | Cambridge Univ. Press |
We run a Combinatorics Study Group during term-time. Please join us if you are visiting London: we meet at 4:30pm on Fridays in room M103 in the Mathematical Sciences building, Queen Mary, University of London (nearest tube Stepney Green, see map). See the Study Group Homepage for further details including this week's speaker.
At present, I keep the records for the London Algebra Colloquium. These are a virtually complete list of speakers and talks since the establishment of the colloquium on 25 October 1950.
I also keep records for the Queen Mary Pure Mathematics seminar – but these only go back to 2002.
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The Design Research Group page provides information about research here in design theory and related topics. It includes pages devoted to design resources and lecture notes on the Web. It also contains details of our EPSRC-funded project "A Web-based resource for design theory", whose official website is at DesignTheory.org. |
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I am currently the chairman of the British Combinatorial Committee. There is a BCC homepage with details of the Committee's activities. The 22nd British Combinatorial conference was held at the University of St Andrews, 5-10 July 2009. The next conference will be at the University of Exeter on 3-8 July 2011. See also the list of forthcoming conferences in combinatorics and related areas, or the on-line British Combinatorial Bulletin. |
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One of the best things about being a mathematician is the opportunity to travel. I have kept various travel diaries. There are some other diaries here too, including Chapter 1 of my autobiography and a readable version of my 2008 G. C. Steward Lectures at Cambridge.
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Apart from this now stressful profession, I used to run (I ran the London
Marathon twice in the late 80s, best time 2:46:59), but now I spend time
walking along the footpaths and |
Miscellanea:
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This problem was considered by Sharad Sane and me over 20 years ago: we failed to solve it. Sharad raised it again at the recent combinatorics conference in Cochin. It is connected with the Erdős–Lovász problem about maximal cliques of r-sets. Given a 2-(v, k, 1) design (that is, a collection of k-subsets of a v-set with the property that any two points lie in exactly one of the subsets), the point set is covered by the r=(v-1)/(k-1) passing through a given point. Show that, if the design is not a projective plane (that is, if r>k), then the point set can be covered by a set of at most r blocks not of this form. The assertion is easy to prove for k≤3. |
I have a collection of old problems, with annotations. See the problem index. Further links to problem pages can be found here.
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School of Mathematical Sciences Queen Mary, University of London Mile End Road London E1 4NS U.K.
Email: P.J.Cameron@qmul.ac.uk |
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On leaving Stepney Green station, turn left, continue for 400 metres along Mile End Road to the Mathematical Sciences building.
If coming by bus, take the number 25 or 205: the nearest stop is Ocean Estate, a request stop between Stepney Green Station and Queen Mary College.
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The views and opinions expressed in this page are mine. The College does not have editorial control over this page and does not endorse, warrant or take responsibility for its content, including the first quote below. The contents may change at any time! |
This page has received
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Clearly we must explain more forcibly, especially at the highest levels of government, that the primary goal of universities is teaching and research, and that income is a constraint, and not the value to be maximised. Andrew Graham, Balliol College Register, 2005. |
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We who often glorify our tendency to ignore reason, installing in its place blind faith, valuing it as spiritual, are forever paying for its cost with the obscuration of our mind and destiny.
Rabindranath Tagore |
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Many teachers will say that 'you cannot express the inexpressible', and they do not try. But teachers like Yasutani and Maezumi don't agree, and I feel as they do: if you perceive deeply enough, a clear and simple way to express it can be found. Tetsugen (Bernard Glassman), quoted in Peter Matthiessen, Nine-headed Dragon River, Shambhala 1998. |
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As Don Braben so aptly put it, funding the technology but not the basic research on which it depends is "living off the seedcorn". Leslie Ann Goldberg |
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When scientists order elements by molecular weight, the elements do not respond by trying to sneak higher up the order. But when administrators order scientists by prestige, the scientists tend to be less passive. Jevin D. West, Nature 456 (2010). |
This page maintained by Peter J. Cameron
P.J.Cameron(AT)qmul.ac.uk
Revised 26 August 2010
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of Britain. A list of "named" walks I have completed is available
