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Friday, October 23, 2015

**Abstract:** A surface evolves by a geometric flow if some geometric quantity (shape, curvature, metric, etc.) changes accrording to a partial differential equation. The study of such geometric flows combines geometry and analysis to gain further insight into the underlying geometry and topology of a surface. In this talk we’ll discuss flow by mean curvature of a surface: one of the first such geometric flows investigated. We’ll also discuss how this PDE can be re-interpreted as a gradient flow of surface area, where each point moves in such a direction that the surface area is minimized. We’ll also discuss how easily this PDE becomes singular, and some current questions relating to singularity analysis of the flow."