Colloquium Mathematics - R.I. van der Veen - University of Groningen

Title: Visualising differential forms

Abstract:

Much of multivariate calculus, (and geometry and PDE) can be
(re)written in terms of Cartan's formalism of differential forms.
For example in this language Maxwell's equations look like dF = d*F = 0
While attractive since it is independent of the choice of coordinate
system, it can be difficult to keep track of
the geometric meaning through all the layers of algebra involved.
The purpose of this talk is to redefine differential forms in a more
geometric way that comes with a simple trick to visualise them in
terms of level sets.
We will start from scratch requiring only basic calculus and linear
algebra and sketch how
wedge product becomes intersection, exterior derivative represents
boundary and Hodge star is just taking orthogonal complement.
At the end of the talk we will return to Maxwell's equations which
should now make more geometric sense.
This is joint work with Jules Jacobs (Delft).