Quantum self-similar groups
David Robertson (University of New England)
Thursday 30th April 16:00-17:00
Maths 116
Abstract
A self-similar group is one which acts faithfully on an infinite homogeneous rooted tree in such a way that the restriction of an element to any subtree acts like another element of the same group. These groups have attracted immense interest for providing solutions to a number of long-standing mathematical problems, most notably answering the General Burnside problem and providing the first known examples of groups with intermediate growth. I will show how self-similar groups can be constructed from certain complex rational functions by iterating the monodromy action, and demonstrate a number of concrete examples. Finally, I will investigate how self-similarity might manifest itself in the world of compact quantum groups and describe some natural examples.
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