Mathematics Colloquia and Seminars

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Spectral Sequences are an algebraic tool that can be used to calculate the (co)homology of many algebraic and topological complexes. More specifically it is an algorithm that involves taking succesive (co)homology groups of a complex. Standard convergence theorems can be established to show that a spectral sequence can "approximate" the (co)homology of the original complex. We will see examples of spectral sequences, including how to naturally induce a spectral sequence from a filtration of a complex. Time permitting we will see the Leray-Serre spectral sequence (invented by Leray as a prisoner of war!) and how it can be used to calculate the (co)homology of the total space of a fibration give the (co)homologies of the base and fiber space.