Abstract: Given the right conditions (enough "space", proper support, etc) the distribution of a typical random walk on a group will spread out. It can be shown that the rate at which such a random walk 'gets lost' is dependent on the volume growth rate of the group (think of it as a dimension). If the group does not have enough "space" for the random walk to "get lost", for example on the sphere, it will spread out as much as it can until it approaches uniform distribution. The rate at which this occurs is also interesting. Side topics discussed will include: The Drunkard Problem, Hitchhiker's Guide to the Galaxy and Magnetic Resonance Imaging.

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If you are interested in giving a talk, please contact Dr. Juan Gil, the Colloquium Coordinator for the Fall 2005 semester.