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Explore the concept of B∞-algebras and their significance in mathematics and physics in this 53-minute lecture from the Workshop on "Non-commutative Geometry meets Topological Recursion" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the algebraic structure of B∞-algebras, which encode higher multibraces and homotopy associativity, first introduced by Baues in relation to iterated loop spaces. Examine the famous example of a B∞ structure on the Hochschild cochain complex and its crucial role in proving Deligne's Hochschild cohomology conjecture. Learn about ongoing research investigating the emergence of canonical B∞-algebra structures on algebras with independent differential graded algebra structures. Discover connections to Koszul's L∞ brace hierarchy in closed string theory and explore related work by Börjeson, Markl, and Loday-Ronco. Gain insights into this complex mathematical topic presented by Maria Immaculada Gálvez Carrillo, with assistance from Carlos I. Pérez Sánchez in the video creation.
