The theory of stacks is the study of symmetries of geometric objects and, as such, has wide impact throughout mathematics: it is a central theme in current work in algebraic geometry, algebraic topology, number theory, analytic and differential geometry, and mathematical physics. Indeed, the theory has proved flexible enough to apply to any field of mathematics were it is important to study symmetries across continuous families of geometric objects, especially when the groups of self-symmetries can vary non-continuously throughout the family. This workshop, to be held at the Fields Institute in Toronto, will bring together leading researchers, postdoctoral mathematicians, and graduate students from fields which apply the theory of stacks; the intent is to discuss recent advances, and to explore and stimulate potentially important new areas of applications. The main speakers will address current problems in chromatic stable homotopy theory, orbifolds, mathematical physics, geometry in various forms, and the emerging field of derived algebraic geometry. Researchers who have agreed to participate include Mark Behrens (MIT), Ian Grojnowksi (Cambridge), Jacob Lurie (Harvard), Gabriele Vezzosi (Firenze), and Angelo Vistolli (Scuola Normale Superiore). In addition, Mike Hopkins (Harvard) will give a series of lectures concurrently with this workshop.
The workshop will be the central event of a two-month subprogram entitled ``Stacks in geometry and topology'', within the thematic program ``Geometric applications of homotopy theory''. The full program will run from January through June of 2007 at the Fields Institute. Beyond the workshop, there a directly related mini-courses by Paul Goerss (Northwestern), Ezra Getzler (Northwestern), and Jacob Lurie (Harvard). The workshop and the mini-courses will pursue the theory of stacks across a diverse fields of mathematics where this theory has been applied, and an important goal of this whole program is to foster cross-disciplinary interaction.
