A Conference that Counts

How many ways are there to arrange a bagful of multicolored M&M candies? What patterns can one identify and what properties do these arrangements have?

Of course, one could try to list all the ways and then count them, but how is one sure that all arrangements have been listed and none have been repeated? Combinatorics, an increasingly important mathematical discipline, is concerned with efficient ways to solve much more sophisticated problems of this sort. It is a branch of mathematics dealing with discrete patterns and counting.

Thanks to a conference co-sponsored by ICTP and the Institute for Studies in Theoretical Physics and Mathematics (IPM), nearly 140 young scientists and mathematicians from throughout the developing world gathered at Trieste to network and learn of the many developments in and applications of combinatorics and graph theory from distinguished international experts.

Topics included graphs and hypergraphs; spectral graph theory; combinatorial designs and matrices; and algebraic combinatorics and permutations.

According to conference co-organizer Richard Brualdi, the international nature of the conference provided a unique opportunity for mathematicians from the developing world to network with one another and learn about some of the latest in a field that has become increasingly important and popular in the last 50 years, thanks partly to the advent of computers.

"Algorithmic procedures are needed in computer calculations, and this is where combinatorics helps," explained Brualdi, a mathematics professor at the University of Wisconsin-Madison.

Brualdi expressed his hope that the conference attendees would come away from the conference with more than newly gained knowledge. "From talking with the conference participants--for example, from Haiti, Ethiopia, Malawi and many other places--I have seen what difficult situations they are in: they have nobody back home to discuss mathematics with, while trying to be productive mathematicians involved in research sometimes under difficult circumstances. I am hoping that every one of them will have developed some contacts as a result of being here so that they can reduce their isolation," he said, adding, "I think it is a wonderful thing what the ICTP is doing and I am glad I was able to contribute in some small way."

The ICTP-IPM Workshop and Conference in Combinatorics and Graph Theory ran from 3 to 14 September. For more details, visit its website.