In the 1960's Edmonds first called attention to an apparent dichotomy between the (polynomially) solvable problems and other problems, which he conjectured to be unsolvable. He also proved that several important models associated with graph matching and matroids are solvable, and observed an apparent connection between solvability and the existence of certain of these structures. In the ensuing thirty years there has been increasing recognition, both of the importance of his results and the validity of his hypothesis. But there have also been explanations of his results, such as the connection between submodular functions and convexity, and beautiful extensions, including submodular function minimization, submodular flows, bisubmodular functions, submodular coverings, matroid parity, delta-matroids, jump systems, path-matchings, valuated matroid intersection. These have led to the solution of problems in areas as diverse as network design and algebraic complexity.

The objective of this workshop is to bring together researchers from various areas with the goal of finding further connections, extensions and applications for these models.

Invited speakers and participants include:

• Andras Frank, E�tv�s University, Budapest
• Satoru Fujishige, Osaka University
• Jim Geelen, University of Waterloo
• Bert Gerards, CWI, Amsterdam
• Bertrand Guenin, Fields Institute and University of Waterloo
• Pavol Hell, Simon Fraser University
• Satoru Iwata, Osaka University
• Bill Jackson, Goldsmith College
• Tom McCormick, University of British Columbia
• William McCuaig, Burnaby, British Columbia
• Kazuo Murota, Kyoto University
• U.S.R. Murty, University of Waterloo
• James Oxley, Louisiana State University
• Alexander Schrijver, CWI and University of Amsterdam
• Andras Seb�, CNRS, Grenoble
• Robin Thomas, Georgia Institute of Technology