Leavitt path algebras, B-infty-algebras and Keller’s conjecture for singular Hochschild cohomology

I will first recall the relation between Leavitt path algebras and the singularity categories of radical-square-zero algebras. Using Leavitt path algebras, we confirm Keller’s conjecture for any radical-square-zero algebra: there is an isomorphism in the homotopy category of $B_\infty$-algebras between the Hochschild cochain complex of the dg singularity category and the singular Hochschild cochain complex of the algebra. Moreover, we prove that Keller’s conjecture is invariant under one-point (co)extensions and singular equivalences with levels. This is joint with Huanhuan Li and Zhengfang Wang.