Min-max theory for the Allen-Cahn equation was developed by Guaraco and Gaspar-Guaraco. Allen-Cahn min-max theory provides a PDE based alternative to the Almgren-Pitts min-max theory for the min-max construction of minimal hypersurfaces. In my talk, I will briefly describe the Almgren-Pitts and the Allen-Cahn min-max theory and discuss the question to what extent these two theories agree. Part of the talk will be based on the above mentioned works of Guaraco and Gaspar-Guaraco.

Bio: Akashdeep Dey earned his Ph.D. from Princeton University in 2022, under supervision of Fernando Codá Marques. He is now a postdoctoral fellow in the University of Toronto.