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 Zimmer. The conjecture states that there can exist symmetries (specifically higher-rank lattices) in a higher dimension that cannot exist in lower dimensions.

A proof of the conjecture was announced in 2017 and published in 2020 by Aaron Brown [de], Sebastián Hurtado-Salazar, and David Fisher [de].^[1]^[2]^[3]

References

1 2 Hartnett, Kevin (2018-10-23). "A Proof About Where Symmetries Can't Exist". Quanta Magazine. Retrieved 2018-11-02.
↑ Brown, Aaron; Fisher, David; Hurtado, Sebastian (2020). "Zimmer's conjecture for actions of $\operatorname {SL} (m,\mathbb {Z} )$ ". Inventiones Mathematicae. 221 (3): 1001–1060. arXiv:1710.02735. doi:10.1007/s00222-020-00962-x. MR 4132960.
↑ "New Methods for Zimmer's Conjecture". IPAM. Retrieved 2018-11-02.

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[Hartnett_2018-1] 1 2 Hartnett, Kevin (2018-10-23). "A Proof About Where Symmetries Can't Exist". Quanta Magazine. Retrieved 2018-11-02.

[2] Brown, Aaron; Fisher, David; Hurtado, Sebastian (2020). "Zimmer's conjecture for actions of $\operatorname {SL} (m,\mathbb {Z} )$ ". Inventiones Mathematicae. 221 (3): 1001–1060. arXiv:1710.02735. doi:10.1007/s00222-020-00962-x. MR 4132960.

[3] "New Methods for Zimmer's Conjecture". IPAM. Retrieved 2018-11-02.

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References