[SAG] Inequalities of Miyaoka-type and Uniformisation of Minimal Varieties of Intermediate Kodaira Dimension

In this talk we present, for any integers $0\leq \nu \leq n$, a set of inequalities satisfied by the Chern classes of any minimal complex projective variety of dimension $n$ and numerical dimension $\nu$. In the cases where $\nu$ is either very small or very large compared with $n$, this recovers many previously known results, notably of Miyaoka and others. We demonstrate that these inequalities are sharp by providing an explicit characterisation of those varieties achieving the equality; our proof, in particular, resolves the Abundance conjecture in this situation. This talk is partly based on joint work with Masataka Iwai and Shin-ichi Matsumura.