## Hodge Theory

### Prof. Ugo Bruzzo

- Preliminaries

Complex manifolds. Kahler manifolds. Sheaves (reminder). - Hodge decomposition

Elliptic operators and cohomology. Hodge and Lefschetz decomposition. Hodge structures. - Spectral sequences

Filtered complexes and associated spectral sequences. The spectral sequence associated with a double complex. Applications. - De Rham cohomology of complex manifolds Hypercohomology. Holomorphic de Rham complex. Applications to Hodge theory.

Reference text:

C. Voisin, Theorie de Hodge et geometrie algebrique
complexe, Societe' mathematique de France 2002