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Martin Bridson (Oxford)
Wednesday 16 November 2011, 14:15-15:15
Profinite completions, curvature, and decision problems
- 👤 Speaker: Martin Bridson (Oxford)
- 📅 Date & Time: Wednesday 16 November 2011, 14:15 - 15:15
- 📍 Venue: MR13, CMS
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Burt Totaro
Abstract
In 1970 Grothendieck asked: if G_1 and G_2 are finitely presented, residually finite groups, and there is a map between them that induces an isomorphism of profinite completions, must the original map be an isomorphism? Fritz Grunewald and I showed that the answer is “no”. Our solution opens up a rich array of possibilities around the questions: how different can G_1 and G_2 be? and what additional hypotheses force G_1 to be isomorphic to G_2? I shall describe recent progress on these questions, explaining in particular how dramatically the algorithmic complexity of G_1 and G_2 can differ.
Series This talk is part of the Algebraic Geometry Seminar series.
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