Ebook: Surveys in Differential Geometry (Volume 13): Geometry, Analysis and Algebraic Geometry

Contents Special Lagrangian fibrations, wall-crossing, and mirror symmetry (Denis Auroux) Sphere theorems in geometry (Simon Brendle and Richard Schoen) Geometric Langlands and non-Abelian Hodge theory (Ron Donagi and Tony Pantev) Developments around positive sectional curvature (Karsten Grove) Einstein metrics, four-manifolds, and conformally Kähler geometry (Claude LeBrun) Existence of Faddeev knots (Fengbo Hang, Fanghua Lin, and Yisong Yang) Milnor K2 and field homomorphisms (Fedor Bogomolov and Yuri Tschinkel) Arakelov inequalities (Eckart Viehweg) A survey of Calabi-Yau manifolds (Shing-Tung Yau)