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Wednesday, November 16, 2005

**Abstract:** Projective algebraic varieties have many special topological properties. In this talk, we will explore some of these properties of complex projective manifolds and present some of their applications (like the classification of the homotopy types of complete interesections of hypersurfaces). Time allowing, we will also look at the topology of varieties defined over subfields of the complex numbers (for example, the homotopy type of their complex points depends on the choice of embedding of the subfield, even though the homology type does not).