- If you are interested in the course but cannot come on Friday,
please email me your "busy times" as we will agree on a time
on that Friday.

- Also, if you want to attend the course or just keep informed about it, please email me as I will be forming an email address list which I will use to send future information.

The course will deal with the geometric aspects of Brownian motion (the fundamental stochastic process) in Euclidean space such as, which sets the Brownian motion can intersect, the Hausdorff dimension of various related sets, the self-intersection behavior of Brownian motion and (if time permits) relationships to potential theory. A tentative outline of the topics which will be covered are:

- Brownian motion
- Kakutani's criterion of which sets are hit by a Brownian motion
- Hausdorff dimension of Brownian motion paths in R^n
- Hausdorff dimension of the zero set of Brownian motion in R
- Self-intersection properties of Brownian motion paths (where the critical dimension turns out to be 4)
- Solution of the Dirichlet problem using Brownian motion
- Relationship between packing dimension and Brownian motion paths

Kursexaminator: Jeff Steif (steif@math.chalmers.se)

Kursliterature: A collection of notes, class notes and some papers.

Last modified: Mon Feb 4 12:53:07 MET 2002