A major 2000 paper of Tian's dealt with the Yang–Mills equations. In addition to extending much of Karen Uhlenbeck's analysis to higher dimensions, he studied the interaction of Yang-Mills theory with calibrated geometry. Uhlenbeck had shown in the 1980s that, when given a sequence of Yang-Mills connections of uniformly bounded energy, they will converge smoothly on the complement of a subset of codimension at least four, known as the complement of the "singular set". Tian showed that the singular set is a rectifiable set. In the case that the manifold is equipped with a calibration, one can restrict interest to the Yang-Mills connections which are self-dual relative to the calibration. In this case, Tian showed that the singular set is calibrated. For instance, the singular set of a sequence of hermitian Yang-Mills connections of uniformly bounded energy will be a holomorphic cycle. This is a significant geometric feature of the analysis of Yang-Mills connections.