Richard Douglas Canary



Address:


Department of Mathematics
University of Michigan
Ann Arbor, MI 48109
(734)-763-5861



Employment:


Stanford University        1989 - 1991

Gabor Szëgo Assistant Professor of Mathematics

University of Michigan        1991 - Present

Assistant Professor of Mathematics        1991 - 1996
Associate Professor of Mathematics        1996 - 2001
Professor of Mathematics                          2001 - Present



Education:


Princeton University        1984 - 89

Ph.D. in Mathematics, June 1989
Thesis: Hyperbolic Structures on 3-manifolds with Compressible Boundary
Advisor: Bill Thurston

Warwick University, Coventry, England        1983 - 84

M.S. in Mathematics, July 1985
Thesis: A Boy's Guide to William P. Thurston
Advisor: David Epstein

New College of USF        1980 - 83

B.A. in Mathematics, June 1985
Advisor: Soo Bong Chae



Visiting Positions:

Mathematics Institute, University of Warwick, April 1993-July 1993
Ecole Normale Superieure de Lyon, May 1994-July 1994
Stanford University, September 1994-August 1995
Mathematical Sciences Research Institute, Berkeley, January 1995-June 1995
Institut Henri Poincaré, Paris, June 1996
University of Southampton, June-July 1997
Wesleyan University, September-December 2004
Mathematical Sciences Research Institute, Berkeley, August-December 2007
Institut de Mathématiques de Toulouse, May 2009
Institut Henri Poincaré, Paris, February-March 2012
Mathematical Sciences Research Institute, Berkeley, January-May 2015



Awards:


Sloan Foundation Fellowship, 1993-1997.
Fellow of American Mathematical Society, 2015.
Sigma Xi Distinguished Lecturer, 2015-2017.


Papers:


[1] (with D.B.A. Epstein and P. Green) ``Notes on notes of Thurston'', in Analytical and Geometrical Aspects of Hyperbolic Spaces, Cambridge University Press, 1987, 3-92.
[2] ``The Poincaré metric and a conformal version of a theorem of Thurston,'' Duke Mathematical Journal 64(1991), 349-359.
[3] ``On the Laplacian and the geometry of hyperbolic 3-manifolds,'' Journal of Differential Geometry, 36(1992), 349-367.
[4] ``Ends of hyperbolic 3-manifolds,'' Journal of the American Mathematical Society, 6(1993), 1-35.
[5] ``Algebraic convergence of Schottky groups,'' Transactions of the American Mathematical Society, 337(1993), 235-258.
[6] ``Geometrically tame hyperbolic 3-manifolds,'' in Differential Geometry: Riemannian Geometry, Proceedings of Symposia in Pure Mathematics, 54(1993), Part 3, 99-109.
[7] (with E. Taylor) ``Kleinian groups with small limit sets,'' Duke Mathematical Journal 73(1994), 371-381.
[8] (with M. Burger) ``A lower bound on l0 for geometrically finite hyperbolic n-manifolds,'' Journal für die reine und angewandte Mathematik, 454(1994), 37-57.
[9] ``Covering theorems for hyperbolic 3-manifolds,'' Proceedings of Low-Dimensional Topology, International Press, 1994, 21-30.
[10] ``A covering theorem for hyperbolic 3-manifolds and its applications,'' Topology, 35(1996), 751-778.
[11] (with Y. Minsky) `` On limits of tame hyperbolic 3-manifolds,'' Journal of Differential Geometry, 43(1996), 1-41.
[12] (with J.W. Anderson) ``Cores of hyperbolic 3-manifolds and limits of Kleinian groups,'' American Journal of Mathematics, 118(1996), 745-779.
[13] (with J.W. Anderson, M. Culler and P. Shalen) ``Free Kleinian groups and volumes of hyperbolic 3-manifolds,'' Journal of Differential Geometry, 44(1996), 738-782.
[14] (with J.W. Anderson) ``Algebraic limits of Kleinian groups which rearrange the pages of a book,'' Inventiones Mathematicae, 126(1996), 205-214.
[15] (with E.C. Taylor) ``Hausdorff dimension and limits of Kleinian groups,'' Geometric and Functional Analysis, 9(1999), 283-297.
[16] (with Y. Minsky and E. Taylor) ``Spectral theory, Hausdorff dimension and the topology of hyperbolic 3-manifolds,'' Journal of Geometric Analysis, 9(1999), 18-40.
[17] (with J.W. Anderson) ``Cores of hyperbolic 3-manifolds and limits of Kleinian groups II,'' Journal of the London Mathematical Society, 61(2000), 489-505.
[18] (with J.W. Anderson and D. McCullough) ``On the topology of deformation spaces of Kleinian groups,'' Annals of Mathematics, 152(2000), 693-741.
[19] ``The conformal boundary and the boundary of the convex core,'' Duke Mathematical Journal, 106(2001), 193-207.
[20] (with J.W. Anderson) ``The visual core of a hyperbolic 3-manifold,'' Mathematische Annalen, 321(2001), 989-1000.
[21] (with M. Bridgeman) ``From the boundary of the convex core to the conformal boundary,'' Geometriae Dedicata, 96 (2003), 211-240.
[22] (with M.Culler, S. Hersonsky, and P. Shalen) ``Approximation by maximal cusps in boundaries of deformation spaces,'' J. Diff Geom., 64 (2003), 57-109.
[23] (with D. McCullough) ``Homotopy equivalences of 3-manifolds and deformation theory of Kleinian groups,'' Memoirs of the A.M.S., 172 (2004), no. 812, xii+218 pp.
[24] (with S. Hersonsky) ``Ubiquity of geometric finiteness in boundaries of deformation spaces of hyperbolic 3-manifolds,'' American Journal of Mathetmatics, 126 (2004), 1193-1220.
[25] ``Pushing the boundary,'' in In the Tradition of Ahlfors and Bers, III, Contemporary Mathematics vol. 355(2004), American Mathematical Society, 109-121.
[26] (with M. Bridgeman) ``Bounding the bending of a hyperbolic 3-manifold,'' Pac. J. Math., 218 (2005), 299-314.
[27] (with P. Bonfert-Taylor, G. Martin and E. Taylor) ``Quasiconformal homogeneity of hyperbolic manifolds,'' Mathematische Annalen, 331 (2005), 281-295.
[28] (edited with D.B.A. Epstein and A. Marden) Fundamentals of Hyperbolic Manifolds: Selected Expositions, London Mathematical Society Lecture Note Series 328, Cambridge University Press, 2006, xii+335 pages.
[29] (with D.B.A. Epstein and P.L. Green) ``Notes on notes of Thurston,'' a re-issue of [1] which appears in [28] with a new foreword by R.D. Canary, 1--115.
[30] (with C. Leininger) ``Kleinian groups with discrete length spectrum,'' Bull. L.M.S., 39 (2007), 189-193.
[31] (with P. Bonfert Taylor, M. Bridgeman, and E.C. Taylor) ``Quasiconformal homogeneity of hyperbolic surfaces with fixed-point full automorphisms,'' Math. Proc. Camb. Phil. Soc., 143 (2007), 71-84.
[32] (edited with J. Gilman, J. Heinonen, and H. Masur) In the Tradition of Ahlfors-Bers, IV, Contemporary Mathematics 432(2007), xvi+229 pages.
[33] ``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.
[34] ``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, Ramanujuan Math. Soc., 2010, 131--150.
[35] (with P. Bonfert-Taylor, G. Martin, E.C. Taylor and M. Wolf) ``Ambient quasiconformal homogeneity of planar domains,'' Ann. Acad. Sci. Fenn., 35 (2010), 275--283.
[36] (with M. Bridgeman) ``The Thurston metric on hyperbolic domains and boundaries of convex hulls,'' Geometric and Functional Analysis , 20 (2010), 1317--1353.
[37] (with P. Bonfert-Taylor, J. Souto and E.C. Taylor) ``Exotic quasiconformally homogeneous surfaces,'' Bull. L.M.S., 43 (2011), 57--62.
[38] (with J. Brock, K. Bromberg, and Y. Minsky) ``Local topology in deformation spaces of hyperbolic 3-manifolds,'' Geometry and Topology, 15 (2011), 1169-1224.
[39] (with P. Storm) ``The curious moduli space of unmarked Kleinian surface groups,'' Amer. J. Math., 134 (2012), 71--85.
[40] (with J. Brock and Y. Minsky) ``The classification of Kleinian surface groups II: the ending lamination conjecture,'' Annals of Mathematics, 176 (2012), 1--149.
[41] (with P. Storm) ``Moduli spaces of hyperbolic 3-manifolds,'' Comm. Math. Helv. 88 (2013), 221--251.
[42] (with M. Bridgeman) ``Uniformly perfect domains and convex hulls: improved bounds in a generalization of a Theorem of Sullivan,'' Pure and Applied Mathematics Quarterly 9 (2013), 49--71.
[43] (with J. Brock, K. Bromberg, and Y. Minsky) ``Convergence of end invariants,'' Geometry and Topology 13 (2013), 2877-2922.
[44] (with P. Bonfert-Taylor and E.C. Taylor) ``Quasiconformal homogeneity after Gehring and Palka,'' Computational Methods and Function Theory (Gehring Memorial Volume), 14 (2014), 417--430.
[45] (with A. Magid) ``Dynamics on PSL(2,C)-character varieties: 3-manifolds with toroidal boundary components,'' Groups, Geometry and Dynamics, 9 (2015), 149--185.
[46] ``Dynamics on character varieties: a survey,'' Handbook of Group Action, Vol.II, L.Ji, A. Papadapoulos, and S.T.Yau, ed., International Press of Boston, 2015, 175--200.
[47] (with M. Bridgeman, F. Labourie and A. Sambarino) ``The pressure metric for Anosov representations,'' Geometric and Functional Analysis, 25 (2015), 1089-1179.
[48] (with J. Brock, K. Bromberg and C. Lecuire) ``Convergence and divergence of Kleinian surface groups,'' Journal of Topology, 8 (2015), 811--841.
[49] (with M. Bridgeman and A. Yarmola) ``An improved bound in Sullivan's convex hull theorem,'' Proceedings of the London Mathematical Society, 112(2016), 146--168.
[50] (with M. Lee, A. Sambarino and M. Stover) ``Amalgam Anosov representations,'' Geometry and Topology, 21(2017), 215--251.
[51] (with M. Bridgeman) ``Renormalized volume and the volume of the convex core,'' Annales de L'Institut Fourier , to appear.
[52] (with M. Bridgeman and A. Sambarino) ``An introduction to pressure metrics for higher Teichmuller spaces,'' Ergodic Theory and Dynamical Systems, to appear.
[53] (with M. Bridgeman) ``Simple length rigidity for Kleinian surface groups and applications,'' submitted.
[54] (with J. Brock, K. Bromberg and Y. Minsky) ``Windows, cores and skinning maps,'' submitted.
[55] (with M. Bridgeman and F. Labourie) ``Simple length rigidity for Hitchin representations,'' submitted.
[56] (with M. Bridgeman, F. Labourie and A. Sambarino) ``Simple root flows for Hitchin representations,'' submitted.
[57] (with J. Brock, K. Bromberg, C. Lecuire and Y. Minsky) ``Local topology in deformation spaces of hyperbolic 3-manifolds II,'' submitted.