Andrew Zimmer
Associate Professor
Department of Mathematics
University of Wisconsin-Madison
Office: 611 Van Vleck
e-mail: amzimmer2[at]wisc.edu
[ cv | research | mentoring]
Research:
I enjoy thinking about geometric structures on manifolds, several complex variables, Riemannian geometry, and discrete subgroups of Lie groups.
Publications / Preprints:
Papers by area: all, several complex variables, discrete subgroups of Lie groups.
Publications involving discrete subgroups of Lie groups:
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Geometry and Dynamics of Transverse Groups (with R. Canary, T. Zhang).
Submitted, 24 pages.
Expository.
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Bi-Lipschitz rigidity of discrete subgroups (with R. Canary, H. Oh).
Submitted, 18 pages.
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Counting, mixing and equidistribution for GPS systems with applications to relatively Anosov groups (with P.-L. Blayac, R. Canary, F. Zhu).
Submitted, 53 pages.
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Patterson-Sullivan theory for coarse cocycles (with P.-L. Blayac, R. Canary, F. Zhu).
Submitted, 72 pages.
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Patterson-Sullivan measures for relatively Anosov groups (with R. Canary, T. Zhang).
Mathematische Annalen, to appear, 41 pages.
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Patterson-Sullivan measures for transverse subgroups (with R. Canary, T. Zhang).
Journal of Modern Dynamics, 20: 319-377, 2024.
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Relatively Anosov representations via flows II: examples
(with F. Zhu).
Journal of the London Math. Society, 109: e12949, 2024 (61 pages).
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Relatively Anosov representations via flows I: theory
(with F. Zhu).
Groups, Geometry, and Dynamics, to appear, 73 pages.
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The structure of relatively hyperbolic groups in convex real projective geometry (with M. Islam).
Algebraic and Geometric Topology, to appear, 31 pages.
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Entropy rigidity for cusped Hitchin representations (with R. Canary, T. Zhang).
Submitted, 57 pages.
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Convex co-compact groups with one dimensional boundary faces (with M. Islam).
Groups, Geometry, and Dynamics, 18: 1145-1183, 2024.
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Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groups (with R. Canary, T. Zhang).
Advances in Mathematics, 404, Part B: 108439, 2022 (67 pages).
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Convex co-compact representations of 3-manifold groups (with M. Islam).
Journal of Topology, 17: e12332, 2024 (56 pages).
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A higher rank rigidity theorem for convex real projective manifolds.
Geometry and Topology, 27: 2899-2936, 2023.
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Convex co-compact actions of relatively hyperbolic groups (with M. Islam).
Geometry and Topology, 27: 417-511, 2023.
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A flat torus theorem for convex co-compact actions of projective linear
groups (with M. Islam).
Journal of the London Math. Society, 103: 470-489, 2021.
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Regularity of limit sets of Anosov representations (with T. Zhang).
Journal of Topology, 17: e12355, 2024 (72 pages).
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Projective Anosov representations, convex cocompact actions, and rigidity.
Journal of Differential Geometry, 119: 161-182, 2021.
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Proper quasi-homogeneous domains in flag manifolds and geometric structures.
Annales de l'Institut Fourier, 68: 2635-2662, 2018.
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Rigidity of convex divisible domains in flag manifolds
(with W. Van Limbeek).
Geometry and Topology, 23: 171-240, 2019.
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Entropy rigidity of Hilbert and Riemannian metrics
(with
T. Barthelmé and
L. Marquis).
International Mathematics Research Notices, 2017 (22): 6841-6866, 2017.
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The structure of projective maps between real projective manifolds.
Geometriae Dedicata, 190: 81-102, 2017
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Characterizing the unit ball by its projective automorphism group.
Geometry and Topology, 20: 2397-2432, 2016
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Rigidity of complex convex divisible sets.
Journal of Topology and Analysis, 10: 817-851, 2018.
Last updated: March 25, 2025.