Organizers: Shaun Fallat (University of Regina), Hadi Kharaghani (University of Lethbridge), Steve Kirkland (University of Regina), Bryan Shader (University of Wyoming), Michael Tsatsomeros (Washington State University), Pauline van den Driessche (University of Victoria).
As noted above, research in combinatorial matrix theory proceeds in a number of diverse directions simultaneously. Not surprisingly, the resulting literature appears in a variety of different journals, primarily those dedicated to linear algebra and those that focus on some aspect of discrete mathematics. A workshop in combinatorial matrix theory would provide a single forum in which recent results are disseminated, frontiers of the discipline are explored, and from which new collaborations could emerge. Such a workshop would not only enable researchers in combinatorial matrix theory to keep abreast of developments central to their own interests, but also expose them to the array of activity taking place at the confluence of matrix theory and combinatorics.
While combinatorial matrix theory has emerged as a vital area of research over the last few decades, there have been few major meetings or workshops devoted solely to the subject - the handful of meetings held in the 1980s and 1990s were small and somewhat regional in scope. However, in January of 2002, a four-day international conference on combinatorial matrix theory was held in Pohang, Korea, attracting some seventy participants. A BIRS workshop on combinatorial matrix theory in 2004 would be the first gathering devoted to combinatorial matrix theory since the Pohang meeting. It would also be the first significant combinatorial matrix theory workshop to be held in North America, and would thus be a great opportunity for those researchers who were unable to attend the Korean meeting. The BIRS workshop itself would benefit from the momentum generated by the Korean conference, and may provide a further impetus for others to host future meetings dedicated to combinatorial matrix theory. We note that the Western Canada Linear Algebra Meeting, which usually takes place in the spring of each even-numbered year, would not be scheduled for 2004 in the event that the proposal for a BIRS combinatorial matrix theory workshop is successful; thus there is no danger of the BIRS workshop competing with an already established series of linear algebra meetings in the region. The workshop will welcome participation not only from established researchers in combinatorial matrix theory, but also from more junior researchers. In particular, graduate students and postdoctoral fellows will be encouraged to attend and participate. The speakers at the workshop will do more than simply report on recent progress. The speakers will also be asked to discuss the direction taken by their particular branch of combinatorial matrix theory: where it has been, where it is going, what challenges lie ahead. These discussions will illuminate combinatorial matrix theory from a number of vantage points - senior researchers, in light of their experience, will provide a broad overview of the road ahead, while junior researchers, in discussing their most innovative work, will suggest the means for navigating that road.
Moreover, the organizers will promote an informal atmosphere to the proceedings, and will ensure that time is allotted for casual discussions. This model has worked well for the series of Western Canada Linear Algebra Meetings (the bulk of the workshop organizers are also organizers for that series), and is effective in enabling the younger researchers to interact with the meeting's more senior participants. In this manner, organizers anticipate that the BIRS workshop will help to bring new researchers into the discipline, and to promote a sense of community within it.
The concrete objectives of this workshop are straightforward. The workshop will provide researchers working in combinatorial matrix theory an opportunity to present accounts of their current research, to identify challenges for the discipline to undertake, and to suggest new approaches to explore; it will serve to establish connections between both individual researchers and between research areas, and so will also promote collaboration and new research. Finally, we have agreed with the editors-in-chief of the Electronic Journal of Linear Algebra that a refereed proceedings of the workshop will appear in that journal.
As combinatorial matrix theory grows, so too does the need for meetings of its community of researchers; the organizers hope that a BIRS workshop will help to meet that need.