Zimmer's conjecture, named for Robert Zimmer, concerns the circumstances under which geometric spaces can exhibit certain kinds of symmetries, specifically actions of higher-rank lattices, stating that such symmetries can exist in sufficiently high dimension but not in lower dimensions. It was proven in 2017 by Aaron Brown, Sebastian Hurtado-Salazar and David Fisher.
Facts
StatementZimmer's conjecture concerns the circumstances under which geometric spaces can exhibit certain kinds of symmetries, specifically actions of higher-rank lattices, and holds that such symmetries can occur only when the dimension of the space is sufficiently high relative to the lattice, not in lower dimensions. 1 Progress Toward ResolutionA proof of the conjecture was announced in 2017 and published in 2020 by Aaron Brown, Sebastián Hurtado-Salazar and David Fisher. 1 Classification
Resolution Status Chronology
Resolved Year Prize Status
Prize Status (category) Connections
In Branch
Source Zimmer's Conjecture (Wikipedia)
Sources
1. Zimmer's Conjecture (Wikipedia)
Lead paragraph, sentence 1
which has to do with the circumstances under which geometric spaces exhibit certain kinds of symmetries
Lead paragraph, sentence 3
A proof of the conjecture was announced in 2017 and published in 2020 by Aaron Brown, Sebastián Hurtado-Salazar, and David Fisher.
- Lead section
In Branch: Geometry, Lead
Zimmer's conjecture is a statement in mathematics "which has to do with the circumstances under which geometric spaces exhibit certain kinds of symmetries." It was named after the mathematician Robert Zimmer.
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