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Hausdorff dimensions of limit sets of Anosov subgroups

Student-Run Research Seminar

Speaker: Subhadip Dey, UC Davis
Location: 2112 MSB
Start time: Tue, Nov 12 2019, 12:30PM

Patterson-Sullivan measures were introduced by Patterson and Sullivan to study the limit sets of Kleinian groups (discrete isometry groups of the hyperbolic n-spaces). Using these measures, they showed a close relationship between the critical exponents (a geometric measurement of the growth of G-orbits in H^n) of Kleinian groups G and the Hausdorff dimensions of the limit sets of G. For instance, when G is convex-cocompact, the above two quantities are equal (Sullivan’79). Anosov subgroups, introduced by Labourie and further developed by Guichard-Wienhard and Kapovich-Leeb-Porti, extend the notion of convex-cocompactness to the higher-rank symmetric spaces. In this talk, we discuss how one can similarly understand the Hausdorff dimension of the limit sets of Anosov subgroups in terms of their appropriate critical exponents. This is a joint work with my advisor Michael Kapovich (https://arxiv.org/abs/1904.10196).