Shifted Poisson geometry of moduli space

In joint work with Sasha Polishchuk (1706.09965), we proved that the moduli space of bounded complexes of vector bundles on a Calabi-Yau d-fold, up to chain isomorphisms, admits a canonical (1-d)-shifted Poisson structure in the sense of Calaque-Pantev-Toen-Vaquie-Vezzosi. When d=1, we classify the derived symplectic leaves for this moduli space. In the consequent work (1712.01659), we use this result to study the Poisson geometry of the matrix algebra over the field of meromorphic functions on an elliptic curve. In particular, we have classified its symplectic leaves. Certain finite dimensional Poisson sub-manifolds of this Poisson ind-scheme are semi-classical limits of generalised Sklyanin algebras.