The string-necklace Lie algebra of a relative Calabi-Yau structure

We review the notion of relative Calabi-Yau structure on a dg functor (a non-commutative analogue of an oriented manifold with boundary introduced in joint work with Toby Dyckerhoff), explain how the Lie algebra of its automorphism group is a chain-level generalisation of the string Lie algebra of Chas-Sullivan and the necklace Lie algebra of Kontsevich, and discuss some examples and applications (part of joint work Nick Rozenblyum).