Busy times, 8: Algebraic graph theory at Villanova

Villanova University

This week, five time zones to the west; next week, three to the east. This week was Andrew Woldar’s conference on algebraic graph theory at Villanova University, a Catholic school founded by Irish Augustinian friars in about 1850. I had never been to Villanova, or even to Philadelphia, the place where the Declaration of Independence and the US Constitution were drafted.

The accommodation was at some distance from the eating place and lecture rooms, so it was necessary to get up and walk across campus before having any coffee (and indeed the coffee in the cafeteria was terrible, though what the conference provided was better).

The conference started at 8:30 on Monday morning; we arrived at about 17:00 on Sunday evening. On the first morning, Rosemary opened the business at 9:00 and I was next at 10:30. There were computer problems: the laptops available refused to show the display on both the computer screen and the projector. Fortunately I was able to ease Andrew’s worries by trying out my laptop and finding it worked perfectly. But the technicians managed to fix the problem with a minute or two to spare.

Sad to say, Andrew fell ill with a high fever on Tuesday and didn’t see any more of the nice conference. We kept getting messages that he was a little better and hoped to be back, but he never quite made it. The conference ran until Thursday with no time off; on Friday, a big alumni reunion was beginning and there was absolutely no room for a mere algebraic graph theory conference.

For me the pick of the plenary talks were two very nice surveys, on the algebraic theory of maps by Gareth Jones, and on Q-polynomial association schemes by Jason Williford. Jason’s talk referred to a paper of mine in 1972; I think the audience were kind enough to offer a collective gasp at the fact that I was publishing papers so long ago!

Apart from the plenaries, there were two parallel sessions. Much of what was on offer was about what some called “association schemes” and others “coherent configurations”: I will write down my thoughts about this terminological problem later. A few of the highlights:

  • Alexander Barg generalised the notion to (infinite) measure spaces, so that instead of requiring various numbers to be constant one requires the measure of the appropriate sets to be constant;
  • Gary Greaves reported some small improvements in published bounds for the number of equiangular lines in Euclidean spaces of various dimensions;
  • Jonathan Smith presented a very general framework for error correction, in which quasigroups arise naturally;
  • Karen Meagher gave a paean to the Erdős–Ko–Rado theorem and versions for permutation groups (she and Chris Godsil are writing a book on this);
  • I liked Mike Newman’s talk showing that factorizations of complete uniform hypergraphs can always be extended to larger complete uniform hypergraphs provided the obvious necessary conditions are satisfied.

At the dinner, Misha Klin gave us an account of the history of algebraic combinatorics in the former Soviet Union. The crucial event was the Vladimir conference in 1991 at which many Western mathematicians were present, and which coincided almost exactly with the putsch which led to the collapse of the Soviet Union.

On Friday, after leaving the room just after breakfast, Rosemary and I went into Philadelphia. Leaving bags was a problem, since there are no public lockers; we had to resort to the (possibly legal) artifact of buying the cheapest Amtrak ticket, on the showing of which we were allowed to leave two bags in their left-luggage office. We went to Independence Mall and saw Independence Hall, but despite keeping my eyes open I didn’t see any independence algebras (nor any Hall algebras, come to that). We didn’t see the Liberty Bell, but went to Christ Church which has another old bell, both of which were made in the Whitechapel Bell Foundry just down the road from where we live. The Christ Chuch bell had been lent to another parish, and they have just got it back 250 years later!

Then to the airport, where the plane was delayed for an hour. As LaTeX might have put it: “Something's wrong, perhaps a missing \item“, and we simply had to wait for the missing item (whatever it was) to be delivered.


About Peter Cameron

I count all the things that need to be counted.
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One Response to Busy times, 8: Algebraic graph theory at Villanova

  1. You can now find videos of the plenary lectures here, and slides of all talks here.

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