Zimmer's conjecture is a statement in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

"which has to do with the circumstances under which

geometric space Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...

s exhibit certain kinds of

symmetries Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...

." It was named after the mathematician

Robert Zimmer Robert Jeffrey Zimmer (born November 5, 1947) is an American mathematician and academic administrator. From 2006 until 2021, he served as the 13th president of the University of Chicago and as the Chair of the Board for Argonne National Lab, Ferm ...

. 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 The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

and David Fisher of

Indiana University Indiana University (IU) is a system of public universities in the U.S. state of Indiana. Campuses Indiana University has two core campuses, five regional campuses, and two regional centers under the administration of IUPUI. *Indiana Universit ...

References

Symmetry Conjectures that have been proved {{math-stub