Liquid crystals are everywhere, and they do more for you than you might think. They tell you the weather, the time, and will kindly let you know that your connection to eduroam was rejected, and that you'll have to listen to the rest of the seminar. Indeed, most displays run on liquid crystals, from the small dials in digital wristwatches to large flat-screen televisions. In this paper, I will review some results pertaining to why (or, perhaps, how) liquid crystals exist in the first place. In particular, I will focus on a model introduced by Heilmann and Lieb in 1979, for which Lieb and I have recently proved the emergence of a nematic liquid crystal phase.
This paper is an informal discussion of the content of [JL17c].