# February Fourier Talks 2007

## Gregory Chirikjian

### Title:

Degenerate Diffusions on Motion Groups: An Application of
Noncommutative
Harmonic Analysis

### Abstract:

Degenerate diffusion equations on the Euclidean motion groups arise in a
number of different fields
including Robotics, Polymer Statistical Mechanics, and Optical
Communications. This talk reviews
several of these application areas and describes how the Fourier transform
of functions on motion
groups can be used to solve these equations. In particular, operational
properties, the convolution
theorem, and Fourier reconstruction formula based on truncated
infinite-dimensional irreducible
unitary representations for these groups are used.