09:00 AM - 09:50 AM
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Quasi-mobius maps between Morse boundaries of CAT(0) spaces
Ruth Charney (Brandeis University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
The Morse boundary of a geodesic metric space is a topological space consisting of equivalence classes of geodesic rays satisfying a Morse condition. A key property of this boundary is quasi-isometry invariance: a quasi-isometry between two proper geodesic metric spaces induces a homeomorphism on their Morse boundaries. In the case of a hyperbolic metric space, the Morse boundary is the usual Gromov boundary and Paulin proved that this boundary, together with its quasi-mobius structure, determines the space up to quasi-isometry. I will discuss an analogue of Paulin’s theorem for Morse boundaries of CAT(0) spaces. This is joint work with Devin Murray.
- Supplements
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09:50 AM - 10:30 AM
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Coffee Break
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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10:30 AM - 11:20 AM
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Cubical accessibility and bounds on curves on surfaces
Nir Lazarovich (ETH Zürich)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
We give a bound on the number of parallelism classes of orbits of hyperplanes in a CAT(0) cube complex which is built from tracks on a simplicial complex. We apply this bound to obtain acylindrical accessibility for actions on CAT(0) cube complexes and bounds on curves on surfaces. Joint work with Benjamin Beeker
- Supplements
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11:40 AM - 12:30 PM
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Harmonic quasiisometries
Dominique Hulin (Université de Paris XI)
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- Location
- --
- Video
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- Abstract
We prove that any quasiisometric map between rank one symmetric spaces is within bounded distance from a unique harmonic map. In particular, this completes the proof of the Schoen-Li-Wang conjecture.
This is joint work with Yves Benoist.
- Supplements
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12:30 PM - 02:30 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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02:30 PM - 03:20 PM
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Cocompactly cubulated Artin groups
Kasia Jankiewicz (University of California, Santa Cruz)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
We exhibit a class of Artin groups that are the fundamental groups of non positively curved compact cube complexes. We show that 2-dimensional or 3-generator Artin groups outside this class are not the fundamental groups of NPCCCs, even virtually. In particular, this includes the braid group on 4 strands. This is joint work with Jingyin Huang and Piotr Przytycki. Similar results have been obtained by Thomas Haettel.
- Supplements
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03:20 PM - 04:00 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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04:00 PM - 04:50 PM
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Artin groups and nonpositive curvature
Thomas Haettel (Université de Montpellier)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Artin groups seem to enjoy several nonpositive curvature features. First, I will explain how braid groups with at most 6 strands act properly and cocompactly on a CAT(0) simplicial complex (joint work with D. Kielak and P. Schwer, following T. Brady and J. McCammond). Secondly, I will describe, more generally than the classical right-angled ones, which Artin groups act properly and cocompactly on a CAT(0) cube complex (related to work of J. Huang, K. Jankiewicz and P. Przytycki).
- Supplements
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