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Friday, October 25, 2013

**Abstract:** In this talk we will introduce an array of spectral sequence used in algebraic topology. The list includes the Serre, Bockstein, Eilenberg-Moore, Adams spectral sequences, and many others. We will introduce the contexts in which these spectral sequences can be used, what is their purpose, and some of the problems that may come up while doing computations with these spectral sequences. Even though the concept of the spectral sequence is algebraic, the underlying gears of it can be given geometric interpretation. We will demonstrate how the questions of algebraic nature have geometric counterparts and how this interaction can be used to our advantage.