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Seminar

RAS - Research Seminar (Part 2): Profinite rigidity and hyperbolic geometry November 16, 2020 (10:00 AM PST - 11:00 AM PST)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Martin Bridson (University of Oxford)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

Video

Profinite Rigidity And Hyperbolic Geometry

Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

Abstract: A finitely generated group G is profinitely rigid (in the absolute sense) if any finitely generated, residually finite group that has the same list of finite quotients as G must actually be isomorphic to G. The first examples of full-sized groups that are rigid in this sense were constructed in 2017 -- they are fundamental groups of 3-dimensional hyperbolic orbifolds with particular arithmetic properties. In this talk I shall explain how ideas from that construction can be extended to prove that certain cocompact Fuchsian groups are profinitely rigid (joint work with Reid, McReynolds and Spitler). I shall begin by sketching the history of profinite rigidity, with key examples, emphasising the connections with hyperbolic geometry (in both the classical and Gromovian senses). I shall end by outlining some of the ongoing work in the field.

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Profinite Rigidity And Hyperbolic Geometry

H.264 Video 25357_28915_8633_Profinite_Rigidity_and_Hyperbolic_Geometry.mp4