\(K\)-Theory from the Ground Up

A 2-hour expository talk given for zygotop in Fall 2023, a learning seminar for young graduate students interested in homotopy theory and related areas. I gave an introduction to algebraic \(K\)-theory, starting from the classical perspective and then spending some time on the universal constructions of connective and non-connective \(K\)-theory (in terms of the universal additive and localising invariant, respectively). I also discussed Waldhausen’s \(wS_\bullet\) construction, and we concluded with a summary of Quillen’s computation of the \(K\)-theory of finite fields via the \(BGL(R)^+\)-construction. Notes are available.