Zimmer's conjecture

{{short description|Conjecture that symmetries exist in higher dimensions that cannot exist in lower dimensions}}

{{Expand language|langcode=fr|date=June 2025}}

Zimmer's conjecture is a statement in mathematics "which has to do with the circumstances under which geometric spaces exhibit certain kinds of symmetries."{{Cite news|url=https://www.quantamagazine.org/a-proof-about-where-symmetries-cant-exist-20181023/|title=A Proof About Where Symmetries Can't Exist|last=Hartnett|first=Kevin|date=2018-10-23|work=Quanta Magazine|access-date=2018-11-02}} 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.{{cite arXiv|last1=Brown|first1=Aaron|last2=Fisher|first2=David|last3=Hurtado|first3=Sebastian|date=2017-10-07|title=Zimmer's conjecture for actions of SL(𝑚,ℤ)|eprint=1710.02735|class=math.DS}}{{Cite news|url=https://www.ipam.ucla.edu/programs/workshops/new-methods-for-zimmers-conjecture/|title=New Methods for Zimmer's Conjecture|work=IPAM|access-date=2018-11-02|language=en-US}}