Constructing and (Not) Computing Algebraic K-Theory

Algebraic K-theory is a rich invariant of rings with connections throughout mathematics. I will motivate and define the 0-th K-group with example computations. Next, we will take a detour through homotopy theory, which will allow us to construct the higher K-groups in a conceptually clear way. These higher groups are notoriously difficult to compute, a challenge I will illustrate through applications to number theory, arithmetic geometry, and/or topology, depending on time constraints and popular demand.