Schedule

5/11/2024 – 12:30 – 14:00, Seminario 1

Title: The Plateau Problem via the Allen-Cahn Equation, I

Abstract: We will spend some time discussing the relation between minimal surfaces and the Allen-Cahn equation with emphasis on the notions of convergence of the level sets of solutions towards minimal surfaces. Next we will introduce the setting for modelling the Plateau problem, this involves working with the equation on a line bundle when near the boundary.

6/11/2024 – 12:30 – 14:00, Seminario 1

Title: The Plateau Problem via the Allen-Cahn Equation, II

Abstract: We go back to some of the technical aspects of the convergence of the level sets but this time on the boundary. We will also present the fundamental solution near the boundary, its stability and discuss some open problems.