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Award ID contains: 1654114

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  1. (, Bulletin of the London Mathematical Society)
    Abstract We prove a finiteness theorem for subgroups of bounded rank in hyperbolic 3‐manifold groups. As a consequence, we show that every bounded rank covering tower of closed hyperbolic 3‐manifolds is a tower of finite covers associated to a fibration over a 1‐orbifold. 
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  2. ; ; ; (, Duke Mathematical Journal)
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  3. ; (, Geometry & Topology)
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  4. ; ; ; ; ; ; (, International Mathematics Research Notices)
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  5. ; ; (, Ergodic Theory and Dynamical Systems)
    We study invariant random subgroups (IRSs) of semidirect products $$G=A\rtimes \unicode[STIX]{x1D6E4}$$ . In particular, we characterize all IRSs of parabolic subgroups of $$\text{SL}_{d}(\mathbb{R})$$ , and show that all ergodic IRSs of $$\mathbb{R}^{d}\rtimes \text{SL}_{d}(\mathbb{R})$$ are either of the form $$\mathbb{R}^{d}\rtimes K$$ for some IRS of $$\text{SL}_{d}(\mathbb{R})$$ , or are induced from IRSs of $$\unicode[STIX]{x1D6EC}\rtimes \text{SL}(\unicode[STIX]{x1D6EC})$$ , where $$\unicode[STIX]{x1D6EC}<\mathbb{R}^{d}$$ is a lattice. 
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  6. ; ; (, International Mathematics Research Notices)
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  7. ; ; ; ; ; ; (, Annals of Mathematics)
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