Lectures: TU and TH 12:50am - 2:10 pm, ROOM TBA.
Instructor: Mark Andrea de Cataldo. Office hours: by appointment.
Tentative Syllabus. Goresky-MacPherson Intersection (co)homology is a geometric-type homology theory which is well suited for the study of singular spaces. I will introduce intersection homology in the ``geometric way," i.e. using chains that meet the strata of a singular space in a controlled way and I will prove the basic properties of this theory, e.g. that it satisfies Poincare' Duality (cohomology does not). I will characterize intersection cohomology in terms of sheaves. This puts the so-colled perverse sheaves in the picture. I will discuss the formalism behind perverse sheaves (derived categories, the geometric functors...) and discuss geometric applications.
Grade: based on in-class participation. The will be no homework and no final exam.
Special needs. If you have a physical, psychological, medical, or learning disability that may impact on your ability to carry out assigned course work, you are strongly urged to contact the staff in the Disabled Student Services (DSS) office: Room 133 in the Humanities Building; 632-6748v/TDD. The DSS office will review your concerns and determine, with you, what accommodations are necessary and appropriate. All information and documentation of disability is confidential. Arrangements should be made early in the semester (before the first exam) so that your needs can be accommodated.