Topological Lower Bounds on the Chromatic Number

In the 1970s, Lovász provided a stunning proof of the Kneser conjecture, which stated that a certain family of graphs had large chromatic number. Lovász proved the result by lower-bounding the chromatic number in terms of the (topological) connectivity of an associated topological space, in arguably the first application of topology to combinatorics. In this talk I'll tell this story, and will hopefully get to tell you about some other applications of topology that are also pure magic.