Office:

Office Phone: **(734) 763-5861**

Title: ** Professor**

canary@umich.edu

Patti Smith (trigger warning: obscenity)

FRG Lecture Series featuring Nicolas Tholozan

Two bumps on a log

Informal Lecture Notes on Anosov Representations (October 10, 2021)

NO GUARANTEES OFFERED. These notes are a work in progress and certainly contain typos, errors and omissions. Comments, criticisms and suggestions are welcome.

``Entropy rigidity for cusped Hitchin representations,'' with Tengren Zhang and Andy Zimmer, preprint.

``Pressure metrics for cusped Hitchin components,'' with Harrison Bray, Lien-Yung Kao , and Giuseppe Martone , preliminary version: preprint.

``Hitchin representations of Fuchsian groups,'' preprint.

``Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groups,'' with Tengren Zhang and Andy Zimmer, Advances in Mathematics, to appear, 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, to appear, revised version: paper (in PDF)

``Pressure metrics for deformation spaces of quasifuchsian groups with parabolics,'' with Harrison Bray and Lien-Yung Kao , Algebraic and Geometric Topology, to appear, 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)

Four generations

Patti Smith's Advice for the Young (trigger warning: obscenity)