Events

Date: 24 March 2026   Time: 14:30 - 15:30

Location: MB503

NOTE: Pre talk intro for non experts starts at 2pm, with seminar starting at 2.30pm

Speaker: Jingeon An, University of Basel.
Title: Minimal surfaces and Allen-Cahn equations.
Abstract: Minimal surfaces and Allen–Cahn equations are central topics in geometric partial differential equations and geometric measure theory. We provide a brief overview of the research history, with particular focus on the interface regularity of Allen–Cahn equations. We then introduce a promising new approach to second-order interface regularity for Allen–Cahn-type equations, based on the new discrepancy–curvature equation ∇· (∇ψ /|∇u|^2) = R, where ψ := F(u)− 1/2 |∇u|^2 is the Modica discrepancy and R is precisely the intrinsic scalar curvature of the level surfaces. Since the above equation holds for any semilinear equation ∆u= F′(u), we expect that this approach is flexible and has broader applications beyond Allen–Cahn equations.