Junior Analysis Seminar – James Tissot (Imperial)

While the Plateau problem was intensely studied throughout the 20th century, leading to multiple influential solutions, the original objective of mathematically modelling soap films remains only partially understood. Indeed, there are many soap films that can be produced experimentally for which there is no robust mathematical existence theory. I will start by introducing the well-known formulations of Plateau’s problem and discussing which soap films they fail to produce. I will then introduce the covering space approach to modelling soap films, originally pioneered by Brakke, and discuss a new result on the existence of families of soap films parametrised by the extent to which they ‘span’ the boundary. Time permitting, I will also discuss shortcomings of this approach in modelling some elusive soap films.