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Applied Mathematics Colloquium
Friday, September 12, 11:30 am
Cullimore Lecture Hall II
New
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Stochastic Models and Lie Groups
Gregory Chirikjian
Department of Mechanical Engineering
Abstract
The theory of random processes is used in a wide variety of applications
ranging from modeling physical Brownian motion to control theory. Many
stochastic problems of interest in engineering and biology involve random
rigid-body motions, which is an example of a Lie group. In this talk, a variety
of stochastic phenomena that evolve on Lie groups will be discussed. These
include the statistical mechanics of DNA and other biopolymers, mobile robot
path planning, and manipulator inverse kinematics. Techniques
from noncommutative harmonic analysis (i.e., Fourier
analysis on Lie groups) is employed to solve evolution equations on Lie
groups that arise in applications.