Counting Simple Closed Curves (Brevan Ellefsen)
Counting closed curves of a given complexity on surfaces is a classic problem, solved by Selberg and others between 1950-1980. However, most of these curves intersect themselves horribly; accordingly, the growth rate for simple closed curves remained an open problem until the 2000s when it was solved by Riven, with more general techniques developed by Mirzakhani. In this talk I will discuss these later developments. I will also briefly discuss what happens one dimension higher. No background is required.