Office Phone: (734) 763-5861
Title: Professor
canary@umich.edu
Patti Smith (trigger warning: obscenity)
NO GUARANTEES OFFERED. These notes are a work in progress and certainly contain typos, errors and omissions. Comments, criticisms and suggestions are welcome.
NO GUARANTEES OFFERED. These notes are (even more so) a work in progress and certainly contain typos, errors and omissions. Comments, criticisms and suggestions are welcome.
``Bi-Lipschitz rigidity of discrete subgroups,'' with Hee Oh and Andy Zimmer, preprint.
``Counting, mixing and equidistribution for GPS systems with applications to relatively Anosov groups,'' with Pierre-Louis Blayac, Feng Zhu and Andy Zimmer, preprint.
``Patterson-Sullivan theory for coarse cocycles,'' with Pierre-Louis Blayac, Feng Zhu and Andy Zimmer, preprint.
``Patterson-Sullivan measures for relatively Anosov groups,'' with Tengren Zhang and Andy Zimmer, preprint.
``Entropy rigidity for cusped Hitchin representations,'' with Tengren Zhang and Andy Zimmer, preprint.
``Patterson-Sullivan measures for transverse groups,'' with Tengren Zhang and Andy Zimmer, Journal of Modern Dynamics, 20(2024), 319--377. preprint.
``Pressure metrics for cusped Hitchin components,'' with Harrison Bray, Lien-Yung Kao , and Giuseppe Martone , Advances in Mathematic, 435(2023), 24 pages, preprint.
``Pressure metrics for deformation spaces of quasifuchsian groups with parabolics,'' with Harrison Bray and Lien-Yung Kao , Algebraic and Geometric Topology, 23(2023), 3615--3653, revised version: paper (in PDF)
``Hitchin representations of Fuchsian groups,'' EMS Surveys in Mathematical Sciences, 9(2022), 355--388 preprint.
``Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groups,'' with Tengren Zhang and Andy Zimmer, Advances in Mathematics, 404(2022), 1--67, preprint.
``Counting, equidistribution and entropy gaps at infinity with applications to cusped Hitchin representation,'' with Harrison Bray, Lien-Yung Kao , and Giuseppe Martone , Crelle's Journal, 791(2022), 1--51, revised version: paper (in PDF)
``Topological restrictions on Anosov representations,'' with Konstantinos Tsouvalas, Journal of Topology, 13(2020), 1497--1520, revised version: paper (in PDF)
``Windows, cores and skinning maps,'' with Jeff Brock, Ken Bromberg , and Yair Minsky, Annales Scientifiques de l'Ecole Normale Superieure, 53(2020), 173--216, revised version: paper (in PDF)
``Simple length rigidity for Hitchin representations,'' with Martin Bridgeman and Francois Labourie , Advances in Mathematics, 360(2020), revised version: paper (in PDF)
``New nonlinear hyperbolic groups,'' with Matthew Stover and Konstantinos Tsouvalas, Bulletin of the London Mathematical Society, 51(2019), 547--553, revised version: paper (in PDF)
``Local topology in deformation spaces of hyperbolic 3-manifolds II,'' with Jeff Brock, Ken Bromberg , Cyril Lecuire, and Yair Minsky, Groups, Geometry and Dynamics, 13(2019), 767--793, revised version: paper (in PDF)
``Simple root flows for Hitchin representations,'' with Martin Bridgeman , Francois Labourie , and Andres Sambarino , Geometriae Dedicata (Goldman Birthday Volume), 38(2018), 57--86, revised version: paper (in PDF)
``An introduction to pressure metrics for higher Teichmuller spaces,'' with Martin Bridgeman and Andres Sambarino , Ergodic Theory and Dynamical Systems, 38(2018), 2001--2035, revised version: paper (in PDF)
``Simple length rigidity for Kleinian surface groups and applications,'' with Martin Bridgeman , Commentarii Mathematici Helvetici, 92(2017), 715--750, revised version: paper (in PDF)
``Renormalized volume and the volume of the convex core,'' with Martin Bridgeman , Annales de L'Institut Fourier, 67(2017), 2083--2098, revised version: paper (in PDF)
``Amalgam Anosov representations,'' with Michelle Lee , Andres Sambarino , and Matthew Stover , Geometry and Topology, 21(2017), 215--251, revised version: paper (in PDF)
``An improved bound for Sullivan's convex hull theorem,'' with Martin Bridgeman , and Andrew Yarmola , Proceedings of the London Mathematical Society, 112(2016), 146--168. revised version: paper (in PDF)
``Convergence and divergence of Kleinian surface groups,'' with Jeff Brock, Ken Bromberg , and Cyril Lecuire, Journal of Topology, 8(2015), 811--841. revised version: paper (in PDF)
``The pressure metric for Anosov representations,'' with Martin Bridgeman , Francois Labourie , and Andres Sambarino , Geometric and Functional Analysis, 25(2015), 1089--1179. revised version (March 2015): paper (in PDF)
``Dynamics on character varieties: a survey,'' Handbook of Group Actions, Vol. II, 2015, 175--200, revised version: paper (in PDF)
``Dynamics on PSL(2,C)-character varieties: 3-manifolds with toroidal boundary components,'' with Aaron Magid, Groups, Geometry and Dynamics, 9 (2015), 149--185. revised version, paper (in PDF)
``Quasiconformal homogeneity after Gehring and Palka,'' with Petra Bonfert-Taylor and Edward C. Taylor , Computational Methods and Function Theory (Gehring Memorial Volume), 14 (2014), 417--430, revised version: paper (in PDF)
``Convergence properties of end invariants,'' with Jeff Brock, Ken Bromberg , and Yair Minsky, Geometry and Topology, 17 (2013), 2877-2922, revised version: paper (in PDF)
``Uniformly perfect domains and convex hulls: improved bounds in a generalization of a Theorem of Sullivan,'' with Martin Bridgeman , Pure and Applied Mathematics Quarterly (Sullivan Birthday Volume) 9 (2013), 49--71, revised version: paper (in PDF)
``Moduli spaces of hyperbolic 3-manifolds and dynamics on character varieties,'' with Peter Storm , Commentarii Mathematici Helvetici, 88 (2013), 221--251, preliminary version: paper (in PDF)
``The classification of Kleinian surface groups II: the ending lamination conjecture,'' with Jeff Brock and Yair Minsky, Annals of Mathematics, 176 (2012), 1--149. Preliminary version: available here
``The curious moduli space of unmarked Kleinian surface groups,'' with Peter Storm , American Journal of Mathematics, 134 (2012), 71--85. preliminary version: paper (in PDF)
``Local topology in deformation spaces of hyperbolic 3-manifolds,'' with Jeff Brock, Ken Bromberg , and Yair Minsky, Geometry and Topology, 15 (2011), 1169--1224. preliminary version: paper (in PDF)
``Exotic quasiconformally homogeneous surfaces,'' with Petra Bonfert-Taylor , Juan Souto , and Edward C. Taylor , Bulletin of the London Mathematical Society, 43 (2011), 57--62. preliminary version: paper (in PDF)
``The Thurston metric on hyperbolic domains and boundaries of convex hulls,'' with Martin Bridgeman , Geometric and Functional Analysis, 20 (2010), 1317--1353. revised version: paper (in PDF)
``Ambient quasiconformal homogeneity of planar domains,'' with Petra Bonfert-Taylor , Gaven Martin, Edward C. Taylor , and Michael Wolf , Ann. Acad. Sci. Fenn., 35 (2010), 275--283. preliminary version: paper (in PDF)
``Introductory Bumponomics: the topology of deformation spaces of hyperbolic 3-manifolds,'' in Teichmuller Theory and Moduli Problem, ed. by I. Biswas, R. Kulkarni and S. Mitra, Ramanujan Mathematical Society, 2010, 131-150, preliminary version: paper (in PDF)
``Marden's Tameness Conjecture: history and applications,'' in Geometry, Analysis and Topology of Discrete groups, ed. by L. Ji, K. Liu, L. Yang and S.T. Yau, Higher Education Press, 2008, 137--162. preliminary version: paper (in PDF)
``Kleinian groups with discrete length spectrum,'' with Chris Leininger, Bulletin of the London Mathematical Society, 39 (2007), 189-193. preliminary version: here
``Quasiconformal homogeneity of hyperbolic surfaces with fixed-point full automorphisms,'' with Petra Bonfert-Taylor, Martin Bridgeman, and Edward C. Taylor, Mathematical Proceedings of the Cambridge Philosophical Society, 143 (2007), 71-84. preliminary version: paper (in PDF)
``A new foreword for `Notes on Notes of Thurston','' in Fundamentals of Hyperbolic Manifolds: Selected Expositions, London Mathematical Society Lecture Note Series 328, Cambridge University Press, 2006, preliminary version: paper (in PDF)
``Quasiconformal homogeneity of hyperbolic manifolds,'' with Petra Bonfert-Taylor , Gaven Martin, and Edward C. Taylor , Mathematische Annalen, 331 (2005), 281-295. preliminary version: paper (in PDF)
``Bounding the bending of a hyperbolic 3-manifold'' with Martin Bridgeman , Pacific Journal of Mathematics, vol. 218(2005), pp. 299-314. revised version: paper (in PDF)
``Homotopy equivalences of 3-manifolds and deformation theory of Kleinian groups'' with Darryl McCullough , Memoirs of the American Mathematical Society, vol. 172(2004), no. 812, preliminary version: paper (in PDF)
``Pushing the boundary,'' In the Tradition of Ahlfors and Bers, III, Contemporary Mathematics vol. 355(2004), American Mathematical Society, 109-121. preliminary version: paper (in postscript) paper (in PDF)
``Ubiquity of geometric finiteness in boundaries of deformation spaces of hyperbolic 3-manifolds,'' with Sa'ar Hersonsky , American Journal of Mathematics, vol. 126(2004), pp. 1193-1220. preliminary version: paper (in postscript) published version
``Approximation by maximal cusps in boundaries of deformation spaces of Kleinian groups'' with Marc Culler , Sa'ar Hersonsky , and Peter Shalen , Journal of Differential Geometry, vol. 64(2003), pp. 57-109. preliminary version: paper (in postscript) paper (in PDF)
``From the boundary of the convex core to the conformal boundary'' with Martin Bridgeman , Geometriae Dedicata, vol. 96(2003), pp. 211-240. preliminary version: paper (in postscript), paper (in PDF without pictures)
``The visual core of a hyperbolic 3-manifold,'' with Jim Anderson , Mathematische Annalen, vol. 321(2001),pp. 989-1000. preliminary version: abstract (in html), paper (in postscript), paper (in PDF)
``The conformal boundary and the boundary of the convex core,'' Duke Mathematical Journal, vol. 106(2001), pp. 193-207. preliminary version: abstract (in html), paper (in postscript) paper (in PDF)
``On the topology of deformation spaces of Kleinian groups,'' with Jim Anderson and Darryl McCullough , Annals of Mathematics, vol. 152(2000), pp. 693-741. paper (in PDF)
``Cores of hyperbolic $3$-manifolds and limits of Kleinian groups II,'' with Jim Anderson , Journal of the London Mathematical Society, vol. 61(2000), pp. 489-505. preliminary version: abstract (in html), paper (in postscript), paper (in PDF)
``Spectral theory, Hausdorff dimension and the topology of hyperbolic 3-manifolds'', with Edward C. Taylor and Yair N. Minsky , Journal of Geometric Analysis, vol. 9(1999), pp. 17-40. preliminary version: abstract (in html), paper (in PDF)
``Hausdorff dimension and limits of Kleinian groups,'' with Edward C. Taylor , Geometric and Functional Analysis, vol. 9 (1999), pp. 283-297. preliminary version: abstract (in html), paper (in postscript)
``Covering theorems for hyperbolic 3-manifolds,'' Proceedings of Low-Dimensional Topology, International Press, 1994, 21-30. preliminary version: paper (in PDF)
Patti Smith's Advice for the Young (trigger warning: obscenity)
