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Title:
Conformal Uniformization of CLE Carpets
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Abstract:
The development of Schramm-Loewner Evolutions, and other related objects, have lead to an explosion in the understanding of various conformally invariant scaling limits of discrete models from statistical physics. Of particular interest for this talk is the development of the conformal loop ensembles (CLE) gaskets which are designed to serve as the scaling limits of the outer cluster boundaries of various spin models. In parallel, there has been much development in the theory of quasi- conformal unifomization, which aims to give meaning to questions like, "what is a version of the Riemann mapping theorem for the Sierpinski carpet?"
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