Even though, in a formal sense, the theory of Lie groupoids is equivalent to the theory of (say differentiable) stacks, the two communities have been working mostly independently of each other. The techniques developed by both schools are quite different from one another, even though similar fundamental questions are being addressed.

One objective of the workshop is to bring together the groupoid community and the stack community to encourage more interaction and cross fertilization between the two fields. This is becoming more and more urgent as both fields progress deeper. To this purpose we plan to include a series of introductory lectures to both theories (groupoids and stacks), to facilitate communication between the fields, and write-ups of these lectures might be of interest to a more general audience.

We believe that the lack of such an opportunity for interaction would actually be detrimental to both fields.

On the other hand we plan to have the main emphasis of the workshop on expositions of recent research. We also wish to bring to the workshop physicists working on quantum field theory and string theory, since physics has been a steady source of ideas in these subjects.

For instance, in the study of Poisson groupoids, there arose the notion of Courant algebroids, which is in some sense a homotopy Lie algebra. There is much evidence that there is a close connection between gerbes and Courant algebroids. Courant algebroids are also likely to be connected with Chiral algebras and vertex algebras, which have been studied mainly by algebraic geometers, for example, Beilinson and Drinfeld and many others. It is very important to bring together the two groups of mathematicians to clarify the connections.

For another example, consider mirror symmetry, which is currently maybe the most exciting web of conjectures in geometry. Stacks are the fundamental tool on the algebro-geometric side of the theory, but deformation quantization is also a central concept. We expect a much better understanding of the intricacies of mirror symmetry to emerge by bringing together experts in the two fields.

There are many bright young people working in these subjects and this workshop will be a great opportunity to disseminate their ideas and to broaden their perspective. We anticipate inviting about 5 to 10 postdoctoral mathematicians to the workshop.