Combinatorial Design Theory (08w5098)


(University of Victoria)

Esther Lamken (Independent)

Richard Wilson (California Institute of Technology)


The Banff International Research Station will host the “Combinatorial Design Theory” workshop next week, November 9 - November 14, 2008.
Combinatorial design theory is the study of arranging elements of a finite set into patterns (subsets, arrays) according to specified rules. It is a field of combinatorics with close ties to several other areas of mathematics including group theory, the theory of finite fields, the theory of finite geometries, number theory, combinatorial matrix theory, and graph theory, and with a wide range of applications in areas such as information theory, statistics, computer science, biology, and engineering. Like most areas of combinatorics, design theory has grown up with computer science and it has experienced a tremendous amount of growth in the last 20--25 years. The field has developed subfields and groups depending on the main techniques used: combinatorial, algebraic, and algorithmic/computational. There are also groups primarily involved with applications such as in coding theory, cryptography, and computer science. As design theory has grown, researchers have become increasingly specialized and focused in subfields. In recent years, design theory has also become quite interdisciplinary with researchers found in both mathematics and computer science departments as well as occasionally in engineering or applied mathematics groups and in industrial groups.

The primary objective of this workshop is to gather together researchers of all levels from different groups and from several different areas of design theory in one place. The goal of the workshop is the exchange of new ideas and techniques in
the different areas of design theory. We hope that the workshop will lead to new connections between areas and new techniques that can be used to solve both purely theoretical problems and problems arising in applications. We expect that the workshop will also lead to better communication between areas and groups in design theory and will give people a broader view of the field (and maybe new collaborators), particularly the younger researchers. The talks planned span the field of design theory and they include applications in computer science and information theory. Each participant will have the
opportunity to speak on their work. Discussion sessions have been planned to focus on special areas of interest, open problems, and on very new results.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).