Manin products of operads in non-associative and chiral algebras

The black and white Manin products of binary quadratic operads present a natural generalization of the same-named constructions for quadratic associative algebras. In this talk, we discuss some problems in non-associative algebra whose solutions involve the Manin products of operads corresponding to varieties of algebras. The systems under consideration include (non-associative) differential algebras, Rota–Baxter algebras, totally and linearly compatible algebras, and chiral algebras in the sense of A. Beilinson and V. Drinfeld.