Algebraic Geometry Student's Seminar : A Leisurely Introduction to Algebraic K-Theory

This talk contains a surface-level overview of algebraic K-theory and related topics. We begin by motivating the construction of $K_0$ of a ring via the Serre-Swan theorem, which connects vector bundles and topological K-theory with projective modules. Then, we construct $K_1, K_2$ and give examples. Next, we introduce Quillen's constructions for higher K-groups via classifying spaces. Time permitting, we may discuss combinatorial aspects of K-theory.