  In this paper, we present a geometric description of foams, which are
prevalent in topological quantum field theories (TQFTs) based on quantum
algebra, and reciprocally explore the geometry of Rozansky-Witten (RW) theory
from an algebraic perspective. This approach illuminates various aspects of
decorated TQFTs via geometry of the target space $X$ of RW theory. Through the
formulation of the Knizhnik-Zamolodchikov (KZ) equation within this geometric
framework, we derive the corresponding braiding and associator morphisms. We
discuss applications where the target space of RW theory emerges as the Coulomb
branch of a compactified 6d SCFT or Little String Theory, with the latter being
particularly intriguing as it results in a compact $X$.
