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Abstract:
For a finitely presented group, the quest to understand the complexity of the
word problem began with Max Dehn about 100 years ago. His fundamental
questions started the subject of combinatorial group theory. One of the most
natural measures of the complexity of a finitely presented group Γ is the
Dehn function, δ(x), which bounds the number of relations one must
apply to a word w that is equal to the identity in Γ to reduce it
to the empty word. In this talk we will see the definition of Dehn functions
and how they are the analog of isoperimetric functions in geometry. Then we
will present a new construction of groups with interesting Dehn functions, the
so-called snowflake groups. The latter construction is joint work with
Noel Brady, Martin Bridson and Max Forester.
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