Static and Dynamic Properties of Surfaces

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The research proposed here is a continuation of the previous grant, aimed at understanding the statistical mechanics and dynamics of a variety of surfaces and interfaces. There are various interesting and fundamental issues, relevant to many different fields that remain to be probed. Most of these questions fall into the following broad categories: (1) Random Manifolds, such as polymers and membranes, obtained from embeddings in a higher dimensional space. (2) Evolving interfaces, such as a growing crystal facet, swelling gel, or a flowing sandpile. (3) Interfaces and Paths in Random Media are relevant to studies as diverse as the trapping of flux lines in a dirty superconductor, to the interference of Feynman paths in a doped semiconductor.