ultrafilters show up in many places, including logic, topology, and analysis. despite this, the concept does not seem to be well-known among mathematicians (indeed, the speaker completed several years of graduate school without learning about them). the goal of this talk is to present a friendly introduction to ultrafilters and to highlight a few of their various manifestations. if all goes well, the talk will include a topological proof of arrow’s impossibility theorem, a classic result from political science.