##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Christos Mantoulids

#### MIT

## Minimal surfaces via the Allen--Cahn equation

##### Abstract:

Minimal surfaces (critical points of the area functional) have a rich and successful history in the study of the interaction between geometry and topology that goes back to the 1960s. In practice, the presence and properties of minimal surfaces inside a Riemannian manifold profoundly influences the ambient geometry. In this talk, we will discuss how one can use the Allen--Cahn equation to guarantee the existence of a rich class of geometrically and topologically distinct minimal surfaces inside a generic Riemannian 3-manifold. As a byproduct, one obtains a pure PDE resolution of a number of previously unapproachable questions in minimal surface theory, which parallels recent simultaneous advances that instead use geometric measure theory.

Host: Lei Ni

### December 2, 2019

### 3:00 PM

### AP&M 6402

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