• Dmitri Panov: Polyhedral characterization of CP^n
    Polyhedral Kahler manifolds are complex manifolds that are built from a collection of Euclidean simplexes, they admit a flat Kahler metric that acquires singularities along a collection of divisors. We will discuss different situations where polyhedral Kahler metrics can be used, including rigidity results on positively curved polyhedral manifolds, construction of complex surfaces of CAT(0) type, and properties of extremal line arrangements.

    The references:
    arXiv:1010.1448 Complex surfaces with CAT(0) metrics
    arXiv:0901.1840 Polyhedral Kahler Manifolds