The Ninth SIAM Conference on Discrete Mathematics was held in Toronto between July 12th to 15th. This is a conference that happens every other year covering all aspects of Discrete Mathematics and its Application areas. The talks in the conference are of three types: Invited talks, Mini symposiums and Contributed papers. I find the mini symposium idea interesting. Each mini symposium focuses on one topic and is organized by one or two persons. These organizers take the responsibility of inviting four to five speakers for the session. The talks in the session typically cover various complementary areas of the symposium topic. The contributed papers are selected from the submissions and the proceedings contain only the abstracts, including those of the mini symposium and invited talks.
Among the invited talks this year, Douglas Stinson gave a talk on two problems on key distribution patterns and non-adaptive group testing algorithms and their connections to frameproof codes. Given a bunch of geometric objects (say points in the plane) and their visibility information, visibility graph can be obtained easily. Sue Whitesides, in another invited talk talked about the other direction -- given a graph, when does it represent the visibility information of some geometric objects? Noga Alon gave an impressive talk on how spectral techniques (algorithms to compute efficiently eigen vectors and eigen values of graphs) are useful for the design of some graph algorithms. William Cook discussed some recent computational advances on the Traveling Salesman Problem. On another invited talk Richard Karp mentioned several combinatorial problems arising out of the genome mapping. He pointed out some of the problems theoreticians are solving are far abstracted from the real problem, as always the fundamental issue is the separation of signal from noise. He also pointed out that there will be many more combinatorial problems arising in the analysis of gene expression data. In another invited talk, Michel Goemans talked about the recent uses of semidefinite programming in Combinatorial Optimization. The highlight, I think, was the talk by Robin Thomas who outlined his recent result proving that the even directed circuit problem and a few related problems have polynomial time algorithms. There was also a talk by Vera Sos on interaction between number theory and combinatorics. This was a talk dedicated to the memory of Paul Erdos.
There were 21 mini symposium sessions and 15 contributed sessions (yes, it was a real mela!). The mini symposium topics covered a lot of areas in Discrete Mathematics from Approximation Algorithms to Isoperimetric inequalities. I gave a talk on `Parametric Tractability Techniques' in the mini symposium on Parameterized Complexity. Obviously there were typically four to five parallel sessions at any time (except during the invited talks). So I attended only a few of the sessions, and it is hard to describe about even them in detail. There were several sessions on Approximation Algorithms and Graph Theory and there was even one on recent applications of Regularity Lemma. Some of the other session topics are: Hamiltonicity, Networks, Randomized Algorithms, Graph Coloring, Scheduling, Matroid Representation, Computational Molecular Biology, Topological Graph Theory and Probabilistic Method.
As one can see, this meeting is considered as a forum for discrete mathematics researchers all over the world, and in North America in particular, to meet in a relaxed atmosphere and exchange their findings. One can see serious researchers ranging from Karp to Alon attending even the contributed paper sessions. Though we don't have such a large community, I think, our National Seminar can be organized along the lines of this meeting. I was particularly impressed with the idea of mini symposiums. Another thing that struck me was the participation of a large number of women researchers.