Zimmer's conjecture

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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 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[change | change source]

  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".