Résume | Derived representation schemes are a derived version of spaces of finite dimensional representations of an associative algebra. I will review this theory, as introduced by Berest, Khatchatrian and Ramadoss, and concentrate on examples associated with quivers. I will discuss how this theory produces new (mostly conjectural) combinatorial identities generalizing Macdonald's identities and how it is related to Nekrasov's partition functions and the K-theory of Nakajima varieties. The talk is based on joint works with Y. Berest, M. Müller-Lennert, S. Patotski, A. Ramadoss, T. Willwacher and the doctoral thesis of S. D'Alesio. |