Wednesday, April 1, 2020
04/01/2020 - 4:15pm
Minimal surfaces are mathematical models for soap films and boundaries of black holes. They are natural critical points of the area functional. In the 1960s, Almgren initiated a program toward a Morse theory for the area functional to prove the existence of abundant minimal surfaces. This program was tremendously advanced by Pitts and Schoen-Simon in the 1980s, and by Marques-Neves and others in the past 10 years. In particular, a satisfying Morse theory has been established. I will survey this beautiful theory with an emphasis on a key step in this program, the long standing Multiplicity One Conjecture, which I solved last year.