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Zimmer's conjecture

Conjecture that symmetries exist in higher dimensions that cannot exist in lower dimensions

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. 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.

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References

Hartnett, Kevin (2018-10-23). "A Proof About Where Symmetries Can't Exist". Quanta Magazine. Retrieved 2018-11-02. https://www.quantamagazine.org/a-proof-about-where-symmetries-cant-exist-20181023/ ↩
Hartnett, Kevin (2018-10-23). "A Proof About Where Symmetries Can't Exist". Quanta Magazine. Retrieved 2018-11-02. https://www.quantamagazine.org/a-proof-about-where-symmetries-cant-exist-20181023/ ↩
Brown, Aaron; Fisher, David; Hurtado, Sebastian (2017-10-07). "Zimmer's conjecture for actions of SL(𝑚,ℤ)". arXiv:1710.02735 [math.DS]. /wiki/ArXiv_(identifier) ↩
"New Methods for Zimmer's Conjecture". IPAM. Retrieved 2018-11-02. https://www.ipam.ucla.edu/programs/workshops/new-methods-for-zimmers-conjecture/ ↩