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:

  1. Bi-Lipschitz rigidity of discrete subgroups (with R. Canary, H. Oh).
    Submitted, 18 pages.
  2. Counting, mixing and equidistribution for GPS systems with applications to relatively Anosov groups (with P.-L. Blayac, R. Canary, F. Zhu).
    Preprint, 55 pages.
  3. Patterson-Sullivan theory for coarse cocycles (with P.-L. Blayac, R. Canary, F. Zhu).
    Preprint, 66 pages.
  4. Patterson-Sullivan measures for relatively Anosov groups (with R. Canary, T. Zhang).
    Submitted, 40 pages.
  5. Patterson-Sullivan measures for transverse subgroups (with R. Canary, T. Zhang).
    Journal of Modern Dynamics, to appear, 46 pages.
  6. Relatively Anosov representations via flows II: examples (with F. Zhu).
    Submitted, 51 pages.
  7. Relatively Anosov representations via flows I: theory (with F. Zhu).
    Submitted, 67 pages.
  8. The structure of relatively hyperbolic groups in convex real projective geometry (with M. Islam).
    Submitted, 30 pages.
  9. Entropy rigidity for cusped Hitchin representations (with R. Canary, T. Zhang).
    Submitted, 57 pages.
  10. Convex co-compact groups with one dimensional boundary faces (with M. Islam).
    Submitted, 24 pages.
  11. 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).
  12. Convex co-compact representations of 3-manifold groups (with M. Islam).
    Journal of Topology, 17: e12332, 2024 (56 pages).
  13. A higher rank rigidity theorem for convex real projective manifolds.
    Geometry and Topology, 27: 2899-2936, 2023.
  14. Convex co-compact actions of relatively hyperbolic groups (with M. Islam).
    Geometry and Topology, 27: 417-511, 2023.
  15. 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.
  16. Regularity of limit sets of Anosov representations (with T. Zhang).
    Submitted, 58 pages.
  17. Projective Anosov representations, convex cocompact actions, and rigidity.
    Journal of Differential Geometry, 119: 161-182, 2021.
  18. Proper quasi-homogeneous domains in flag manifolds and geometric structures.
    Annales de l'Institut Fourier, 68: 2635-2662, 2018.
  19. Rigidity of convex divisible domains in flag manifolds (with W. Van Limbeek).
    Geometry and Topology, 23: 171-240, 2019.
  20. Entropy rigidity of Hilbert and Riemannian metrics (with T. Barthelmé and L. Marquis).
    International Mathematics Research Notices, 2017 (22): 6841-6866, 2017.
  21. The structure of projective maps between real projective manifolds.
    Geometriae Dedicata, 190: 81-102, 2017
  22. Characterizing the unit ball by its projective automorphism group.
    Geometry and Topology, 20: 2397-2432, 2016
  23. Rigidity of complex convex divisible sets.
    Journal of Topology and Analysis, 10: 817-851, 2018.

Last updated: May 02, 2024.