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Wild and tame behaviour in group theory

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Two parallel stories in the study of (infinite, discrete) groups unfolded in the 20th century. On the one hand, clever combinatorial techniques made it possible to encode Turing’s halting problem into group presentations; the upshot is that, in the worst case, groups can exhibit very wild behaviour. On the other hand, an influx of geometric techniques showed that a generic group is quite tame. In this talk, I’ll attempt to tell this story, and describe some of my own contributions.

This talk will be followed by a wine reception in Pav. E Common Room (venue for reception TBC )

This talk is part of the CMS Colloquia series.

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