In this talk, I will present parts of a recent paper written
jointly with Mario Garcia-Fernandez and Jeff Streets ("NonKahler Calabi-Yau
Geometry and Pluriclosed Flow" arxiv:2106.13716). In particular, I intend to
discuss long-time existence and convergence of solutions to pluriclosed flow
on manifolds satisfying a flatness condition. As the pluriclosed flow does
not admit a scalar reduction in general, I will introduce the language of
holomorphic Courant algebroids and a result of J.M. Bismut that will allow
us to derive apriori estimates for an equivalent coupled
Hermitian-Yang-Mills-type flow.