Abstract: We will briefly recall Poisson structures in the algebraic geometry context. We will focus on two main classes of examples: moduli space of sheaves on del Pezzo surfaces and semi-classical limits of noncommutative deformations.

Abstract: We will give a unified construction of the algebraic Poisson structures mentioned in the first part of the talk, via the moduli space of complexes on degeneration of elliptic curves. Our construction leads to a neat description of the symplectic leaves. We will discuss several applications on deformations of Hilbert schemes and positroid varieties.