A successful collaboration that resulted in a proof of homological mirror symmetry would provide researchers with a way to translate between seemingly disconnected mathematical realms.

Exploring a Deep Symmetry Among Unrelated Space-Times

Homological mirror symmetry proof would relate seemingly disconnected mathematical realms

Calabi-Yau manifold
Calabi-Yau manifolds, such as the one shown, set the framework for mathematicians to begin working on the homological mirror symmetry conjecture.

Mathematics could be forgiven for thinking itself a fairy godmother to the other sciences, sprinkling useful theories and theorems into biology, chemistry and physics, and thereby enabling them to reach new heights. Sometimes, however, the benefits go the other way. The Simons Collaboration on Homological Mirror Symmetry, launched in late 2015, focuses on a field of mathematics inspired by theoretical physics, specifically string theory.

‘Mirror symmetry’ refers to an unexpected correspondence between seemingly unrelated space-times. The goal of the collaboration is bold: to prove mirror symmetry in its full generality. A successful proof would have a large and immediate effect on mathematics, with the potential to make difficult questions in symplectic geometry or complex geometry more tractable. It would have surprising and paradigm-changing effects in other areas as well.

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