Abstract: These are lecture notes that grew from tutorial lectures given in conjunction with the program on Nanoscale Material Interfaces held at the Institute for Mathematical Sciences, National University of Singapore. Contents include discussion of: Domain-wall dynamics in the 1D Allen-Cahn equation; Proof of universal self-similar behavior in a mean-field model of 1D domain growth; Monopole model of 3D Ostwald ripening via restricted gradient flow; Kohn-Otto method for rigorous bounds on coarsening rates; Dynamic scaling analysis for Smoluchowski's coagulation equation.

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