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Thursday, July 14, 2016

**Abstract:** Algebraic K-Theory assigns topological invariants to rings, by studying invertible matrices (with coefficients in that ring) all at once. Historically, it does so by a construction of Grothendieck, which assigns a ``group'' to a set with an operation, and does so in a universal way. We will discuss some basic examples of rings, the Grothendieck group construction on them, and what information algebraic K-theory holds in general.