Noncommutative global Kosul duality and homotopy theory

可微分次Koszul对偶是一个影响深远的现象，它将代数和幂等余代数的行为联系在一起，似乎是非常不同的对象。在有理同伦理论和形变理论方面，人们对它进行了大量的研究。最近观察到，可以构造一种比以前观察到的更一般形式的Koszul对偶；它涉及一般的余代数，而不是幂等余代数。这个项目将探索这种全球Koszul二元性的拓扑分支。

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.