Student Colloquium: Martin Winslow
Title: Clifford's Geometric Algebra In Your Face
Abstract: The standard system of "vector analysis" developed by Gibb's in the late 1800's is the most ubiquitous way of expressing geometric information algebraically. Competing theories like Hamilton's "quaternions" have long been supplanted by history's victor. The irony is that both systems have their deficiencies. Clifford's geometric algebra (GA) doesn't suffer from these same deficiencies and, in fact, makes many of them transparent. In 3-D space, the awkwardness between a vector and a "pseudovector" is revealed to be a misinterpretation of a more robust object in a geometric algebra. Ultimately geometric algebras offer a new perspective on many old ideas in Gibb's vector analysis and Hamilton's quaternion algebra, and in natural way, unifies them. The key is the ability to multiply vectors and elements in the algebra together through a unique geometric product. Consequences are explored and advanced notions are touched on.