 CARMA COLLOQUIUM
 Speaker: Dr Michal Ferov, CARMA, The University of Newcastle
 Title: Groups, machines, algae and trees
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Tue, 4^{th} Apr 2017
 Abstract:
In a way, mathematics can be seen as a language game, where we use symbols, together with some rewriting rules, to represent objects we are interested in and then ask what can be said about the sequences of symbols (languages) that capture certain phenomena. For example, given a group G with generators a and b, can we recognise (using a computer) the sequences of generators that correspond to nontrivial elements of G? If yes, how strong computer do we need, i.e. how complicated is the language we are studying?
There is a natural duality between various types of computational models and classes of languages that can be recognised by them. Until recently most problems/languages in group theory were classified within the Chomsky hierarchy, but there are more computational models to consider. In the talk I will briefly introduce Lsystems, a family of classes of languages originally developed to model growth of algae, and show that the coword problem in Grigorchuk's group, a group of particularly nice transformations of infinite binary tree, can be seen as a language corresponding to a fairly simple Lsystem.
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