Zimmer's conjecture is a statement in

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

"which has to do with the circumstances under which

geometric space Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

s exhibit certain kinds of

symmetries Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations ...

." It was named after the mathematician

Robert Zimmer Robert Jeffrey Zimmer (November 5, 1947 – May 23, 2023) was 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 Na ...

. 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 , Sebastián Hurtado-Salazar, and .

References

Dynamical systems Differential geometry Group theory Geometric topology Symmetry Conjectures that have been proved {{math-stub