Analysis on Manifolds (Theory of smooth manifolds) is strictly required; from the definition of smooth manifolds and to differential forms and de Rham cohomology [5]. Knowledge of basic algebraic topology (Fundamental group, Singular homology and cohomology groups) is not strictly required, but is highly recommended. [6]
Holomorphic functions of several variables. Complex manifolds. Examples of period maps. Kahler Package. Lefschetz theorems. Polarized Hodge structures. Cohomology of Manifolds varying in a family. If time permits, we will touch more advanced subjects, such as the geometry of the period domains, and the infinitesimal properties of period maps. [1-4]
By completing this course, you will have command over foundational classical examples of Hodge theory. Additionally, you will learn the basic theoretical concepts and results about Hodge Theory, thus you will be able to study advanced topics in Hodge Theory.
[1] - Period Mappings and Period Domains (J. Carlson et al) [2] - Principles of Algebraic Geometry (P. Griffiths, J Harris) [3] - Hodge Theory and Complex Algebraic Geometry (C. Voisin) [4] - Lectures on the Hodge theory of projective manifolds (A. de Catldo) [5] - Differential Topology (V. Guillemin, A. Pollack) [6] - Algebraic Topology (A. Hatcher)