Symmetries of Graphs and Networks IV

Last week I was at the Symmetries of Graphs and Networks IV conference at Rogla in Slovenia. The conference webpage is here.  At the same time was the annual  PhD summer school in discrete maths. As usual it was a very enjoyable and well organised conference. It was good to catch up with some of the regulars and meet a few new people as well

I was one of the invited speakers and spoke about some of the work that I have been doing recently with Luke Morgan on graph-restrictive permutation groups. The slides are available here.  The two relevant preprints are on the arxiv here and here.





Irsee conference

This week I am at the Finite Geometries: Third Irsee Conference in Irsee, Germany. It is the first leg of a 5 week trip to Europe. I am sure Gordon will be jealous to hear that I managed to use some  of my frequent flyer points to upgrade to premium economy which seemed to be the same seats that they used to have in business class.

I think it is the first geometry conference that I have been to and it has gone very well.  Some highlights so far have been:

  • Michel Lavrauw’s talk on `Finite semifields and nonsingular tensors’. He gave a very accessible introduction (this is the job of a plenary speaker) to the topic including their importance to finite geometry and a bit of the history.
  • Peter Cameron’s talk (as always) on `Geometric problems from synchronization’.
  • Jonathan Jedwab’s talk on `The asymptotic merit factor of binary sequences’. This talk was superb in telling us about the development of the subject as well as some of his recent work. It included a quote from a referee’s report to a grant application that the problem was too hard and they shouldn’t waste their time on it.

Another highlight was the Lied recital by Kris Coolsaet and Jan De Buele which was also accompanied by thunder and lightning and the page turning of Geertrui Van de Voorde.

I spoke about my work with John on groups acting regularly on generalised quadrangles and it seemed to be well received.

Symmetries of graphs and networks

I have just spent the last week at the 2nd International worskshop on Symmetries of Graphs and Networks which was held in Rogla, Slovenia. The first conference in this series,  which I also attended, was held in Banff in November 2008.  Rogla is located on top of a mountain in north east Slovenia and is at about 1500m above sea level, thus keeping what seems to be a tradition of holding such conferences at altitude.  Overall the conference went very well and the organisers should be congratulated for their great efforts.

As well as being a ski lodge in the winter, the hotel here is also used for training camps by many professional and junior sporting teams from Slovenia and nearby. In this spirit the conference included a Slovenia vs The Rest of the World basketball game (which the Slovenians won), a 6 a side soccer tournament and a 4x400m relay. I was the goalkeeper in Marston Conder’s soccer team which by one measure (of course the one that we preferred) won the tournament.

On mathematical matters the conference had 6 keynote talks. Ted Dobson spoke on Normal Cayley Graphs. These are Cayley graphs Cay(G,S) of a group G with joining set S such that the full automorphism group is G\rtimes Aut(G,S) where Aut(G,S) is the group of all automorphisms of G that fix S setwise. The talk included many interesting open problems and a few conjectures, including one that almost all Cayley graphs whose automorphism group is not as small as possible (that is, only G or twice as large as G) are normal Cayley graphs.

Continue reading “Symmetries of graphs and networks”

Binary matroids with no K_5 minor

I gave my talk at the Maastricht workshop yesterday and so here are the slides (Maastricht talk).

Matroid theory is not especially well known (in fact, when he gave a talk here, Brian Alspach used a result from matroid theory and described the subject as “the one that is allocated the smallest and furthest away room in any conference that has parallel sessions”) and so usually it’s necessary to put a lot of basic definitions into any talk. Fortunately this occasion, where everyone is working in matroids, is an exception and so I could launch straight in.

In some sense, binary matroids are a generalization of graphs, and so any question that can be asked about graphs can be asked unchanged about binary matroids. In the 1930s Klaus Wagner proved the famous excluded minor result

A graph is planar if and only if it does not have the complete graph K_5 or the complete bipartite graph K_{3,3} as a minor.

He also gave a description of the graphs that do not have K_5  as a minor, and similarly the class obtained by excluding K_{3,3}.

We (that is,  me and my friends from Wellington NZ, Geoff Whittle and Dillon Mayhew) are trying to extend these two results to binary matroids and get descriptions of the exact structure of those classes. It turned out that the case for excluding K_{3,3} was tractable, though we ended up with a long 113 page paper that has just appeared in the Memoirs of the American Mathematical Society. But excluding K_5 seems much more difficult and we really don’t know where to go from here.

My talk basically describes what we’ve done and where we’re stuck!

33rd ACCMCC talk

This week I am at the 33rd Australasian Conference on Combinatorial Mathematics and Combinatorial Computing at Newcastle, Australia. I am one of the invited speakers and gave the first talk of the conference this morning. I have uploaded the slides for my talk entitled, `Local symmetry properties of graphs‘. It covered s-arc-transitive graphs, locally s-arc-transitive graphs, distance transitive graphs, lcoally distance transitive graphs and locally s-distance transitive graphs. This includes joint work with Alice Devillers, Cai Heng Li and  Cheryl Praeger.

So far several sets of beamer symbols have been spotted.

AustMS conference

I am back after my trip to the annual meeting of the Australian Maths Society in Adelaide. There were 12 plenary speakers this year. Going to one of these general meetings always reveals how big a subject mathematics is and how little of it I know. For this reason I always prefer “big picture” plenaries over more detailed ones. A couple of personal  highlights were Terry Tao’s public lecture on `Structure and randomness in the prime numbers’,  Jacqui Ramagge’s talk on `Totally disconnected, locally compact groups’ which outlined the theory of the subject developed mainly by George Willis,  and Akshay Venkatesh’s talk on his work with Ellenberg and Westerland on `The Cohen-Lenstra heuristics over global fields’.

There were up to 12 parallel sessions on at any given time. I mainly attended the combinatorics session where there were many good talks and  I spoke on `3/2-transitive permutation groups’. I have uploaded the slides for my talk. I  also ventured to the Topological groups session  and enjoyed Daniel Horadam’s talk there on `Automorphism groups of trees’. There were many other talks I would have liked to have gone to but they clashed with other interesting talks or me speaking.

Overall the conference went very well and the organisers should be congraulated on the great job they did. The conference dinner was also very well done: the food and wine was great and there was even a band.

AustMS talk on chromatic roots

I gave my talk at the AustMS 2009 meeting yesterday, and have now uploaded the PDF slides of my talk which was called Chromatic Roots and Maxmaxflow.

I was lucky enough to be the “keynote” speaker at the special session on Combinatorics so I got a one-hour time slot, which is usually easier to deal with than a shorter one.

The talk itself was a more focussed variant of a talk I gave at the British Combinatorial Conference in July this year, and describes my recent work with Alan Sokal, which is essentially complete, but just needs wrestling into final publishable shape. Working with Alan is a tremendous privilege, but exploring every possible generalization, hypothsis-weakening and related application that his incredibly fertile brain  throws up is incredibly time-consuming for a mere mortal!

Anyway the gist of this work is that we want to find a parameter to replace maximum degree in the result that the moduli of chromatic roots are bounded by a function of maximum degree. The parameter maxmaxflow which is defined to be the maximum number of edge disjoint paths between any pair of vertices is a promising alternative, and this talk gives a very general overview of our proof that it works for series-parallel graphs.

Lose the beamer navigation symbols!!

We’re all getting ready here for next week’s Australian Math Society conference in Adelaide, so I’ve been watching a few practice talks. Watching these, along with a few other recent talks,  reminded me of a pet peeve.

Nowadays, even in mathematics conferences, most talks are computer presentations, and most of these are prepared using Till Tantau’s beamer package for LaTeX.

Although beamer is amazingly good – or perhaps because beamer is amazingly good – its sheer ubiquity means that so many talks “look the same”.

And one way in which they look the same is that although I have never seen anyone use them in a talk, almost everyone seems to keep the default navigation symbols at the bottom corner of every page, where they often overlap the content and generally clutter the page.


But it is so easy to turn them off – just add

\setbeamertemplate{navigation symbols}{}

before the beginning of the document and away they go!

Maths talks on the web

I have just come across the Newton Institute’s Web seminars. It looks a great resource of various talks given at the Institute including those given as part of their programmes and workshops. They seem to have  quite an extensive recording mechanism as there appears to be several cameras involved. The files are a bit big but I can see myself wasting hours watching them as long as my australian broadband can cope. The site includes a talk by Gordon.