The goal of these two 90 minutes talks will be to (i) Give an introduction to mean curvature flow (the steepest descent flow for the area of hypersurfaces), and singularity formation in this flow, and to (ii) Introduce and explain in some detail the specific gluing techniques for nonlinear partial differential equations, developed in the context of minimal surfaces (e.g. mean curvature $H=0$), which ultimately lead to construction of new examples of singularity models (solitons).
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