After defining the notion of (mixed) Hodge structure, the first main goal of the course will be to explain the construction (due to Deligne) of a functorial mixed Hodge structure on the cohomology of complex quasi projective algebraic varieties; and the applications of this result for our understanding of the topology of such spaces. The second main goal will be to explain the corresponding variational theory, especially for families of smooth projective varieties over a quasi-projective base: variations of Hodge structures, quasi-unipotence of the local monodromy, theorem of the Fixed Part, semi-simplicity theorem...
The prerequisites for this course are a familiarity with classical cohomology theories (for instance singular cohomology), fundamental groups; a first course in algebraic geometry will help.
Course: Rudower Chaussee 25, Monday 1pm-3pm 3.011, Tuesday 9am-11am 3.006
Exercise: Rudower Chaussee 25, Monday 3pm-5pm 3.011
Course Language: English