Mathematics

The course aims at offering a self-contained introduction to complex differential geometry. The focus will be on showing how complex geometry affords powerful methods to study Riemannian notions, in particular the Ricci curvature. Thus we will start with basic notions of Riemannian geometry, such as curvature and harmonic theory, and then see how these take a special form for the class of compact Kähler manifolds. According to the interests of the audience, more advanced topics may include: Hard Lefschetz Theorem, Ricci flat Kähler metrics and Yau’s proof of Calabi’s conjecture, problems of current interest such as the J-equation and deformed Hermitian Yang-Mills connections.