Prerequisites: Graduate algebra and algebraic topology. For example, you should be familiar with modules over rings, cohomology, and higher homotopy groups.
Course Description: This course will serve as an introduction to spectral sequences as a computational tool. Spectral sequences are high-powered algebraic machines used in a variety of settings. The course will focus on applications to algebraic topology. The main topics include the Serre spectral sequence, constructing spectral sequences via double complexes and exact couples, some applications of spectral sequences, computing some stable homotopy groups of spheres, and the Adams spectral sequence. Time permitting, additional topics include Massey products, Toda brackets, and other spectral sequences such as the Bockstein spectral sequence, etc.
Boris Botvinnik