Abstract：The weighted extremal Kähler metrics introduced by Lahdili provide a vast generalisation of Calabi's extremal Kähler metrics, encompassing many examples of canonical metrics in geometry. In this talk, I will give a quick introduction to these metrics, and discuss the proof that weighted extremal manifolds are relatively weighted K-polystable, in a suitable sense. The proof is along th...
Abstract：According to mirror symmetry, the geometry of a given Fano manifold endowed with some extra data, including an arbitrary Kähler class, should be reflected in a mirror Landau-Ginzburg model, i.e. a noncompact complex manifold endowed with a nonconstant holomorphic function. On the other hand, a fundamental notion for constructing moduli of Fano manifolds is K-polystability, i.e. positi...
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