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VIGRE seminar, Spring 2003: Invariant Subspace Theory

Instructor: Carl Pearcy
Students Enrolled: Ryan Thomas (undergrad math) and Radu Dascaliuc, Sami Hamid, Luan Hoang, Amir Husain, Constantine Onica, Nirin Randrianarivony (grad students in math).
Both graduate and undergraduate students are invited to enroll in the course, which is entitled "The invariant subspace problem for operators on Hilbert space". The prerequisites are a course in linear algebra and a course in the topology of metric spaces. I will spend the first few weeks (if necessary) talking about the background material necessary to understand the problem. Next, I will present certain techniques for producing invariant subspaces for certain classes of operators. Then we will discuss these techniques and consider several open, research problems involving these techniques. I hope that some of the students will make progress on some of these problems, and their results will be presented to the class. This should take us through the semester.