Zimmer's conjecture

Zimmer's conjecture is a statement in mathematics "which has to do with the circumstances under which geometric spaces exhibit certain kinds of symmetries." ^[1] It was named after the mathematician Robert Jeffrey Zimmer. The conjecture states that there can exist symmetries (specifically higher-rank lattices) in a higher dimension that cannot exist in lower dimensions.

In 2017, the conjecture was proven by Aaron Brown and Sebastian Hurtado-Salazar of the University of Chicago and David Fisher of Indiana University.^[1]^[2]^[3]

References

↑ ^1.0 ^1.1 Hartnett, Kevin (23 October 2018). "A Proof About Where Symmetries Can't Exist". Quanta Magazine.
↑ Brown, Aaron; Fisher, David; Hurtado, Sebastian (7 October 2017). "Zimmer's conjecture for actions of $\mathrm{SL}(m,\mathbb{Z})$". arXiv:1710.02735. {{cite journal}}: Cite journal requires |journal= (help)
↑ "New Methods for Zimmer's Conjecture".

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[auto-1] 1.0 ^1.1 Hartnett, Kevin (23 October 2018). "A Proof About Where Symmetries Can't Exist". Quanta Magazine.

[2] Brown, Aaron; Fisher, David; Hurtado, Sebastian (7 October 2017). "Zimmer's conjecture for actions of $\mathrm{SL}(m,\mathbb{Z})$". arXiv:1710.02735. {{cite journal}}: Cite journal requires |journal= (help)

[3] "New Methods for Zimmer's Conjecture".

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