Variation of Hodge Structures

Hodge theory in the geometric sense is a field which lie in the intersection of complex, algebraic and differential geometry and is in particular used in mirror symmetry. The cohomology of compact Kähler manifolds, e.g. smooth projective varities, are the main examples of Hodge structures.

In this talk I want to give a short introduction to Hodge structures and their variations, i.e. abstract definitions and the main examples which are constructed from families of compact Kähler manifolds. After that one could consider period domains and period mappings which are an important tool in complex algebraic geometry.

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