Timo Alho (06/11/15)

Sigurður Örn Stefánsson, November 2, 2015

Math Colloquium

Speaker: Timo Alho
Title: Coordinate-free integrals in Geometric Calculus

Location: V-157, VRII.
Time: Friday, November 6, and Friday, November 13 at 15:00-16:00.

Abstract:

Using the apparatus of geometric algebra and geometric calculus, we introduce a method for evaluating integrals in R^n and its submanifolds without introducing coordinates. The method is based on using the fundamental theorem of geometric calculus repeatedly and cutting the resulting manifolds so as to guarantee the existence of a boundary and an antiderivative at each step. The method is a direct generalization of the usual method of integration on functions of a real variable. It may lead to both practical applications and help unveil new connections to various fields of mathematics.