Noncommutative global Kosul duality and homotopy theory

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Global Koszul duality and applications.Differential graded Koszul duality is a far-reaching phenomenon linking the behaviour of algebras and conilpotent coalgebras, seemingly very different objects. It has been much studied in connection with rational homotopy theory and deformation theory. Recently it has been observed that a more general form of Koszul duality than previously observed, can be constructed; it involves general, as opposed to conilpotent, coalgebras. This project will explore topological ramifications of this global Koszul duality.