Mathematics Colloquium

Venue: Ramanujan Hall, Mathematics Department, Room 214

Date and time: Wednesday, 7 September 2022 at 4 pm

Speaker: Dr. Akashdeep Dey, Princeton University

Title: A comparison of the Almgren-Pitts and the Allen-Cahn min-max theory

Abstract: Min-max theory for the area functional was developed by Almgren
and Pitts to construct closed minimal hypersurfaces in arbitrary closed
Riemannian manifolds. There is an alternate PDE-based approach to the
construction of minimal hypersurfaces. This approach is based on the study
of the limiting behavior of solutions to the Allen-Cahn equation. In my
talk, I will briefly describe the Almgren-Pitts min-max theory and the
Allen-Cahn's min-max theory and discuss the question of to what extent these
two theories agree.

Note: The Mathematics Colloquia are accessible to the general audience.