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.

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

1. 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 (2017-10-07). "Zimmer's conjecture for actions of SL(𝑚,ℤ)". arXiv:1710.02735 [math.DS].
3. "New Methods for Zimmer's Conjecture". IPAM. Retrieved 2018-11-02.