I’ve been on the road: three Canadian provinces and six states (five American, one Australian) in the last two months. My body-clock has no idea what it should be set to, and this morning I found myself utterly befuddled when I woke up in my own bedroom for the first time in months — but the upside is that I’ve been to a couple of really enjoyable meetings.

Combinatorial Potlatch

The Combinatorial Potlatch is a British Columbian/Pacific North-West institution. The word Potlatch refers to a gift-giving festival practised by the indigenous inhabitants of the area, and it was chosen to reflect the informal and hospitable nature of the workshop. I really like the way the meeting is run: it lasts only one day, there are only two or three speakers, and the day ends in the pub. Nobody speaks more than once in the series, ensuring that new people to the area are given a chance to participate. Judging by this year’s meeting, there is also an emphasis on inviting early-career mathematicians. In fact I had the slightly unsettling experience of being the oldest of the speakers: the first time this has happened to me, but probably not the last (if I can be presumptuous enough to expect further invitations).

In its recent incarnation, the Potlatch is organised by Nancy Neudauer and Rob Beezer, both of whom I know from a short course on matroid theory that Nancy ran during the 2011 joint meeting of the AMS and MAA. Every year a university from the region is tapped to host the meeting, and in 2013 it was the turn of Victoria University, the namesake of my own institution. The name of this Victoria is slightly more obvious, as it resides in the town of Victoria, provincial capital of British Columbia, and largest urban area on Vancouver Island. I had been in Vancouver immediately before the meeting, so I caught the ferry, which dodges islands in the Juan De Fuca Strait.

The island is also beautiful. While I was there I got to see some spawning salmon:

Of course, you don’t get to spawn without breaking some fish:

All part of life’s cycle, but it does make for a fairly pungent atmosphere.

I enjoyed the two talks that I got to see at the Potlatch. Richard Hoshino gave an interesting and personal talk about some of his career choices; in particular, his decision to emphasise education and real-world optimisation over pure research that is unlikely to be appreciated or noticed by more than a handful. Speaking for myself, it doesn’t bother me too much that my research will only ever be read by specialists. I think it’s legitimate for artists and pure mathematicians alike to gain satisfaction from doing the best work they can, while letting the audience take care of itself — the number of people who appreciate a piece of work isn’t necessarily the best indication of its quality anyway. But I certainly understand that not everyone feels as I do.

Jérémie Lumbroso gave an attractive talk on an idea that I hadn’t encountered before: if we have a generating function that enumerates a class of combinatorial objects, then we can use that generating function to construct a parameterised random algorithm that will select one of those objects. The choice of parameter will influence the size of the object chosen by the algorithm. Therefore, if we want to randomly select a rooted binary tree embedded in the plane with 20 vertices (say), then we adjust our parameter so that the algorithm will deliver a tree of the right size with reasonable probability, and we let it run until it produces an output with 20 vertices. This process chooses trees of 20 vertices with uniform probability. Jérémie showed us the code that he used to implement the algorithm, and it was remarkably simple: just a couple of lines of Mathematica code.

37ACCMCC

Soon after the Potlatch, it was time for me to head to Perth for the 37th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing. Matroidunion.org’s own Irene Pivotto was a member of the organising committee, and Gordon Royle from SymOmega lead the committee. It was an extremely well-run meeting; so much so, in fact, that you can only feel sorry for the organiser of the 38th conference, given the high standards that he or she will have to live up to. (Expect to see more posts about 38ACCMCC sometime soon.)

I enjoyed many talks at the ACCMCC, so I will mention only the ones with significant amounts of matroid content. Nick Brettell spoke about an algorithm for constructing a $k$-tree of a matroid; Ben Clark talked about a project that myself and Stefan are involved in: the attempt to find excluded minors for the matroids representable over the partial field $\mathbb{H}_{5}$; Rong Chen talked about an inductive connectivity theorem for $k$-coherent matroids; Darryl Funk described work on the excluded minors for the class of frame matroids; Songbao Mo talked about a polymatroidal characterisation of abstract connectivity functions; Peter Nelson’s presentation covered some of the same material as his most recent post; Irene Pivotto spoke about some work she has done with Rong on a class of matroids arising from bias graphs; Michael Welsh described work on a conjecture of Steven Archer on maximum-sized golden-mean matroids. I think that covers everyone, so apologies if I have missed anyone.

The talks I gave at the two conferences were basically isomorphic (so apologies to the two people who were in the audience for both). In the first half I introduced matroids, and talked about excluded-minor characterizations, both exisiting and those still in progress. The second half was dedicated to work I have been doing with Mike Newman and Geoff Whittle on the impossibility of using matroid axioms to capture representability. Here are my slides.

Postscript

Attending these conferences made me think again about a small peeve of mine. I can’t understand the practice of abbreviating one’s own name to an initial when listing the authors of a theorem. You will no doubt know what I mean:

Theorem (M., Newman, Whittle — 2013)

instead of

Theorem (Mayhew, Newman, Whittle — 2013).

Can anyone tell me why we do this? It makes no sense to me. Slides usually have enough room to list names in full, so it can’t be a space constraint. Perhaps it comes from some sense of humility, as if we don’t want to lay too much of a claim to our own work lest we appear immodest? If that’s the case, then we seem to be saying that writing one’s own name above a theorem that we helped prove is an unbearable act of self-aggrandisement, and I can’t agree with that. I think it’s probably more likely that the custom just started years ago, and now people do it because it is what everyone does. But that’s not a good enough reason to continue a tradition. Unless somebody gives a masterful argument in favour of the practice in the comments, then I am going to write my own name in full on my slides, and I think others should do the same.