In deformation theory, a branch of mathematics, Deligne's conjecture is about the operadic structure on Hochschild cochain complex.
Various proofs have been suggested by Dmitry Tamarkin,[1][2] Alexander A. Voronov,[3] James E. McClure and Jeffrey H. Smith,[4] Maxim Kontsevich and Yan Soibelman,[5] and others, after an initial input of construction of homotopy algebraic structures on the Hochschild complex.
[6][7] It is of importance in relation with string theory.