Mathematical Sciences: The Topology of Algebraic Varieties

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Aspects of the topology of algebraic varieties will be studied. Particular emphasis will be on the development of new topological invariants or techniques (e.g. Intersection Homology, Motivic Cohomology, Perverse Sheaves) and on the study of particular varieties which are important in applications (e.g. Modular Varieties, Configuration Spaces). Algebraic varieties are spaces defined by polynomial equations. They should be particularly simple, but their topology can be more complicated than this suggests. Since they arise in many different contexts, it is important to classify and analyze them.