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Sierpinski carpets are interesting fractals that can arise in a dynamical setting as limits sets of Kleinian groups or Julia sets of rational maps. While the topology of Sierpinski carpets is well-understood, difficult problems arise if one investigate their quasiconformal geometry. In my talk I will focus on some recent joint work with M. Lyubich and S. Merenkov on quasiconformal rigidity questions for Sierpinski carpets that are Julia sets of postcritically-finite rational maps.
