Explore conformal field theoretic realizations of infinite-dimensional Lie algebras, including the BMS algebra, in this 56-minute lecture from the Thematic Programme on "Carrollian Physics and Holography" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into ongoing research with PhD student Girish Vishwa, examining the definition of BRST complexes that compute semi-infinite cohomology of these algebras relative to the center with values in a module. Gain insights into cutting-edge work at the intersection of conformal field theory, Lie algebras, and cohomology theory.