The Thomas-Yau conjecture is an open-ended program to relate special Lagrangians
to stability conditions in Floer theory, but the precise notion of stability is
subject to many interpretations. I will focus on the exact case (Stein Calabi-Yau manifolds),
and deal only with almost calibrated Lagrangians. We will discuss how the existence of
destabilising exact triangles obstructs special Lagrangians, under some additional assumptions,
using the technique of integration over moduli spaces.