The “Magic Wand” theorem of Eskin-Mirzakhani and Eskin-Mirzakhani-Mohammadi is a far reaching result regarding the dynamics of an action of the group SL(2, R) on the moduli space of translation surfaces. Its proof (in 2013) was the culmination of many years of work by many authors and employed tools in ergodic theory, probability, group theory, Teichmuller theory, and more. Surprisingly, this result has significant implications for the illumination problem, which is an elementary problem in plane geometry. I will present what is known about the illumination problem, give a (somewhat impressionistic) overview of the Magic Wand theorem, and explain the connection between the two. The talk will be accessible to a wide audience.
