Lectures/PhD course on Hausdorff dimension, capacity, and Brownian
motion 1995/96
I will be giving a set of lectures/Ph.D course
on the above topics in the spring.
All are welcome. I plan on meeting once a week for 2 hours for about 12 weeks
with the period of time probably being weeks 7-20 (although this
is not definite right now). The tentative time is 13:15 on Fridays
in Room S1.
There will be no book but rather I will be giving lectures based on a number
of different sources of which you will get copies. As far as prerequisites,
these are always difficult to determine but it should be enough with measure
and integration theory and some undergraduate probability.
Some of the topics that I would like to cover (at least to some extent) are
- Hausdorff dimension
- capacity
- Frostman theory which links the above 2 concepts
- 1-d Brownian motion: the exact Hölder exponent of sample paths
(which implies the
nowhere differentiability of these paths), law of the iterated
logarithm, etc
- >=2 dimensional Brownian motion: solution of the Dirichlet problem,
solution of Poisson's equation,
exact capacity characterization of sets which are hit by
Brownian motion,
the Hausdorff dimension of sample paths, the existence of double
points in 3-d space but not in 4-d space, the nonexistence of
triple points in 3-d space and the existence of
k-tuple points in 2-d space for all k.
Organizational meeting
February 16, 13:15 Room MD1
Jeffrey Steif
<steif@math.chalmers.se>
Last modified January 22, 1996, by Lars Alexandersson <larsa@math.chalmers.se>