Geometric algebra vs. differential forms

[element4]

Recently I discovered geometric algebra which looks very exciting. I was wondering if there is any connection between geometric algebra and differential forms?

I see that different research groups recommend the use of differential forms (http://www.ee.byu.edu/forms/forms-home.html" ), and claims that these are much more intuitive and have other advantages over the usual vector calculus (of Gibbs).

Do you have good examples of where differential forms and geometric algebra (respectively) will be useful and why? (I mean not only for expressing thing elegantly for example maxwell's equations, but useful in terms of concrete calculations too).

It would be nice to hear about other examples than the usual ones of high energy physics, for example classical physics (fluid mechanics, electromagnetism) and condensed matter physics.

I am currently taking a fantastic course on abstract differential geometry (and we will cover differential forms soon) but i am wondering if geometric algebra are worth studying.

 

[element4]

Bump!

 

[Surprised]

I dare say that proponents would say that each contains the other (both originate from Grassmann).

Personally I prefer GA (ie Clifford Algebra with a real geometric interpretation and including a geometric calculus) but I'm a very concrete/applied sort of person; tastes might vary.