CARMA SEMINAR Speaker: Assoc Prof Murray Elder, CARMA, The University of Newcastle Title: Finding short words in the first Grigorchuk group Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 24th Mar 2011 Abstract: In the 80's R.Grigorchuk found a finitely generated group such that the number of elements that can be written as a product of at most $n$ generators grows faster than any polynomial in $n$, but slower than any exponential in $n$, so-called "intermediate" growth. It can be described as an group of automorphisms of an infinite rooted binary tree, or in terms of abstract computing devices called "non-initial finite transducers". In this talk I will describe what some of these short words/products of generators look like, and speculate on the asymptotic growth rate of all short words of length $n$. This is joint unpublished work with Mauricio Gutierrez (Tufts) and Zoran Sunic (Texas A&M). [Permanent link]