Chromatic (co)homology theories

Homology and cohomology are powerful invariants: while easy to compute, they contain rich information about spaces, the geometry of manifolds, vector bundles, and more. (Co)homology satisfies a list of axioms which are easy to generalize. The best-known generalization is K-theory, but there are many more. In this talk, my goal is to give an introduction to some generalized (co)homology theories that play a central role in modern-day stable homotopy theory and to discuss some of the fascinating phenomena they exhibit.