Recent Progress on Stable Solutions of the Allen–Cahn Equation

Abstract: I will present recent results and open problems concerning stable solutions of the Allen–Cahn equation and its free boundary version. In particular, I will discuss the long-standing problem of classifying stable solutions to the Allen–Cahn equation, both with and without area bounds, in low dimensions, and the consequences of these classifications. I will outline the classical results and highlight more recent developments, emphasizing the main difficulties in the problem and some of the key ideas underlying the proofs of our recent results.

The talk is based on two papers: one joint with Chan, Figalli, and Fernández-Real, and another joint with Florit and Simon.

analysis of PDEsdifferential geometry

Audience: researchers in the topic

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NCTS international Geometric Measure Theory seminar

Series comments: We envisage an event built around virtual presentations on progress in geometric measure theory by external speakers. Every researcher is free to register as a participant and thus gain access to a virtual facility which is complete with lobby, lecture hall, and areas with boards for discussion. Thus, it shall recreate the exchange possibilities found at international conferences.

Focus: regularity and singularity theories for submanifolds of Riemannian manifolds and some of its applications.

Frequency: one presentation every other month.

Registration: required for new participants, go to the seminar website (allow at least one working day for processing).

Virtual venue: HyHyve space NCTS iGMT seminar (only for registered participants, opened one hour before the events).

You might want to consult the description of the premises and instructions.

Former organiser: Guido De Philippis (till March 2022).

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