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Decision Problems in Group Theory

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Part of the TMS Symposium

Around the 1930’s, Alan Turing developed the concept of a Turing machine, the basic framework for what would eventually become modern computation. However, this construction rests on a paradox: such machines cannot always compute their own future behaviour. Such classes of problems are referred to as “incomputable”, and they appear in many areas of mathematics, from set theory, to algebra, and even to geometry and topology. In this talk I will give an overview of Turing’s construction, outline how this gives rise to some incomputable problems in group theory, and give examples of some corresponding incomputable problems in geometry.

This talk is part of the Trinity Mathematical Society series.

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