In planning the ACE 06 workshop, with the exception of aiming for a larger participation, we are to a large extent following the Finnish precedent of a cross between a summer school and a conference. Specifically:

• There will be no parallel sessions,
• The minimum talk length is 30 min. (30-50 min. is ideal),
• There will be plenty of time for discussions,
• There will be a poster session to encourage participation by both graduate students and more senior researchers.
• There is a clear emphasis on cochain methods and geometric aspects.
• The proceedings of the workshop are informal in the sense that the presentations will be collected in electronic form and disseminated electronically. The identification of a coherent theme for an edited volume will be considered formally only after the workshop.

   The inevitable use of Whitney forms within engineering electromagnetics was predicted 20 years ago. In the two decades since, Whitney forms have played a key role in the development of computational electromagnetism; first in Europe, then in Asia, and finally in North America where some DOD labs are regarding them as an essential tool. Unfortunately, this technology transfer from “pure mathematics” to engineering side-stepped traditional applied mathematicians. A major objective in organizing this workshop is to get key mathematicians who have been cited by engineers years ago, to finally rub shoulders with the key players within the engineering community!

Given the emerging themes and applications, the workshop hopes to:

• Bring together engineers, numerical analysts, software developers, and mathematicians who, when viewed in the context of the workshop themes, have made remarkable and lasting contributions in their respective fields.

• Identify the continuing and essential role played by Whitney forms and “Geometric integration theory” in sub-fields of mathematics and in applications, and evaluate effective “technology transfer” to pressing issues in computational electromagnetics. Furthermore, panel discussions may explore the exciting prospect of a “reverse technology transfer” from computational methods to topological problems made computationally tractable by geometric techniques.

• Identify open problems where Whitney form techniques, semi-simplicial techniques, and related algebraic constructions are expected to have a direct impact on the data structures which underlie the algorithms used for the analysis of electromagnetic fields on “unstructured” meshes. Of particular interest are problems which can be resolved without resorting to floating point arithmetic.

For the uninitiated, the above may require some elaboration. Maxwell’s equations, (ME), are most simply stated in integral form. However, key geometric insights are often obscured when ME are considered to be a statement about vector fields, whose components relative to some coordinate system are treated as coupled scalars. The coordinate-free formalism of differential forms may be more obscure in the literature, but it enabled us to appreciate the simple four-dimensional nature of ME a century ago and, by viewing calculus on manifolds in terms of the tools of algebraic topology, cochain methods and, in particular, Whitney forms create a natural setting for computational electromagnetics.