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Disordered materials or equivalent finite-dimensional graph models have associated geometrical objects that are self-affine ("rough") or fractal. Outstanding issues about glassy behavior of materials and the difficulty of solving computational problems can be traced to the complexity of these interfacial objects. I will present an overview of the geometry and topology of such interfaces and their dynamics. This overview will focus on the application of combinatorial optimization algorithms to the study of these complex objects. Host: Misha Chertkov, T-13 |