Complex and Differential Geometry : Conference held at Leibniz Universität Hannover September 14 – 18 2009 This volume contains the Proceedings of the conference Complex and Differential Geometry 2009 held at Leibniz Universität Hannover September 14 18 2009. It was the aim of this conference to bring specialists from differential geometry and (complex) algebraic geometry together and to discuss new developments in and the interaction between these fields. Correspondingly the articles in this book cover a wide area of topics ranging from topics in (classical) algebraic geometry through complex geometry including (holomorphic) symplectic and poisson geometry to differential geometry (with an emphasis on curvature flows) and topology. Participants Surfaces of general type with geometric genus zero: a survey Holomorphic symplectic geometry: a problem list Generalized Lagrangian mean curvature flow in Kähler manifolds that are almost Einstein Einstein metrics and preserved curvature conditions for the Ricci flow Differential Harnack Estimates for Parabolic Equations Euler characteristic of a complete intersection Cremona special sets of points in products of projective spaces Stable bundles and polyvector fields Buser Sarnak invariant and projective normality of abelian varieties Complete K¨ahler Einstein Manifolds Fixed point subalgebras of Weil algebras: from geometric to algebraic Questions Self similar solutions and translating solutions Aspects of conformal holonomy Bifurcation braid monodromy of plane curves A survey of Torelli and monodromy results for holomorphic symplectic Varieties On singularities of generically immersive holomorphic maps between complex hyperbolic space forms Generically nef vector bundles and geometric applications Dolbeault cohomology of nilmanifolds with left invariant complex structure Smooth rationally connected threefolds contain all smooth curves Submanifolds in Poisson geometry: a survey.