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
Awards:
Sloan Foundation Fellowship, 1993-1997.
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] (with J. Brock and Y. Minsky) ``The classification of Kleinian surface
groups II: the ending lamination conjecture,'' submitted.
[29] (with C. Leininger) ``Kleinian groups with discrete length
spectrum,'' Bull. L.M.S., 39 (2007), 189-193.
[30] (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.
[31] (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.
[32] (with D.B.A. Epstein and P.L. Green) ``Notes on notes of
Thurston,'' a re-issue of [1] which appears in [31] with a new
foreword by R.D. Canary, 1--115.
[33] (edited with J. Gilman, J. Heinonen, and H. Masur) In the
Tradition of Ahlfors-Bers, IV, Contemporary Mathematics
432(2007), xvi+229 pages.
[34] ``Introductory bumponomics: the topology of deformation spaces
of hyperbolic 3-manifolds,'' to appear.
[35] ``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.