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
Mathematical Sciences Research Institute, Berkeley, August 2020-April 2021
Awards:
Sloan Foundation Fellowship, 1993-1997.
Fellow of American Mathematical Society, 2015.
Sigma Xi Distinguished Lecturer, 2015-2017.
Simons Fellowship, 2020-2021.
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 l_{0} 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 , 67(2017), 2083--2098.
[52] (with M. Bridgeman) ``Simple length rigidity for Kleinian surface groups
and applications,'' Commentarii Mathematici Helvetici,
92(2017), 715--750.
[53] (with M. Bridgeman and A. Sambarino) ``An introduction to pressure metrics
for higher Teichmuller spaces,'' Ergodic Theory and Dynamical
Systems, 38(2018), 2001--2025.
[54] (with M. Bridgeman, F. Labourie and A. Sambarino) ``Simple
root flows for Hitchin representations,'' Geometriae Dedicata
(Goldman Birthday Volume), 38(2018), 57--86.
[55] (with J. Brock, K. Bromberg, C. Lecuire and Y. Minsky) ``Local topology
in deformation spaces of hyperbolic 3-manifolds II,''
Group, Geometry and Dynamics, 13(2019), 767--793.
[57] (with M. Stover and K. Tsouvalas), ``New nonlinear hyperbolic
groups,'' Bulletin of the London Mathematical Society,
51(2019), 547--553.
[57] (with M. Bridgeman and F. Labourie) ``Simple length rigidity for Hitchin
representations,'' Advances in Mathematics, 360(2020).
[58] (with J. Brock, K. Bromberg and Y. Minsky) ``Windows, cores and
skinning maps,'' Annales Scientifiques de l'Ecole Normale
Superieure, 53(2020), 173--216.
[59] (with K. Tsouvalas), ``Topological restrictions on Anosov
representations,'' Journal of Topology, 13(2020), 1497--1520.
[60] (with H. Bray and L.-Y. Kao) ``Pressure metrics on deformation spaces
of quasifuchsian groups with parabolics,'' Algebraic and Geometric Topology, to appear.
[61] (with H. Bray, L.-Y. Kao and G. Martone) ``Counting, equidistribution and entropy gaps at infinity
with applications to cusped Hitchin representations,'' Crelle's Journal , 791(2022), 1--51.
[62] (with T. Zhang and A. Zimmer) ``Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groups,'' Advances in Mathematics, 404(2022), 1--67.
[63] ``Hitchin representations of Fuchsian groups,'' submitted.
[64] (with H. Bray, L.-Y. Kao and G. Martone) ``Pressure metrics
for cusped Hitchin components,'' submitted.
[65] (with T. Zhang and A. Zimmer) ``Entropy rigidty for cusped Hitchin
representations,''
submitted.