Cohomological physics is particularly manifest in terms of BRST operators Q. In the 1980s, they appeared as providing L∞-algebras in several settings: • Constrained Hamiltonians systems • Lagrangians with symmetries • Higher spin algebras • Closed String Field Theory (CSFT) • Courant algebroids • Double field theory

In most cases, the BRST operator Q is of the form Q = {Ω, } for Ω an element of a graded Poisson/Gerstenhaber algebra. The talk will emphasize the commonality of these examples; a slight familiarity with these terms wouldn't hurt.