The Whitney form revolution in computational electromagnetics, initiated over two decades ago, builds on the mathematics which created discrete Hodge theory, solved the Ray-Singer conjecture and set the stage for Dennis Sullivan's approach to rational homotopy theory. The basic tools point to a discrete framework for Ed Witten's TQFT approach to the Jones polynomial, and associated computational complexity issues. Furthermore, this interaction between electrical engineers and geometrically minded topologists was largely unnoticed by applied mathematicians! ACE '06 will bring together experts in very diverse fields to continue this technology transfer from seemingly pure mathematics to deep problems encountered in enlarging the scope of computational electromagnetics.
Electrical engineers have always marveled at the beauty of Maxwell's theory of electromagnetism and associated mathematical formalism. They have pondered both the practical implications of this big picture, and the difficulties of fitting it into the undergraduate curriculum. The Whitney form revolution of the past two decades has translated the formalism associated with Mawell's equations into a discrete setting, has resolved some of the deepest problems in computational electromagnetics, has lead to very efficient software implementations, has enabled unforeseen applications to be tackled, and has offered open research questions back to 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! By having a diverse set talks, poster sessions, and panel discussions, ACE '06 will sustain the strong level of cross-fertilization by bringing from different countries, a diverse set of experts and academic disciplines, students, professors, and engineers who have grown successful companies. More information can be found on the conference webpage: www.bu.edu/eng/ace2006/
