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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.

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

References

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 (2017-10-07). "Zimmer's conjecture for actions of SL(m,Z)". arXiv:1710.02735 [math.DS].
"New Methods for Zimmer's Conjecture". IPAM. Retrieved 2018-11-02.