**
Exponential Mixing and Smooth Classification of Commuting Expanding Maps
(with L. Yang), accepted by JMD **

**Character Varieties and Actions on Products of Trees**

(with D. Fischer, M. Larsen and M. Stover), accepted by Israel Journal.

**Equilibrium Measures for Certain Isometric Extensions of Anosov Systems**

(with D. Vischer), Ergodic Theory and Dynamical Systems,

Published online: 22 September 2016, pp. 1-14. doi: 10.1017/etds.2016.62.

**On the Work of Rodriguez Hertz on Rigidity in Dynamical Systems**

Journal of Modern Dynamics 10 (2016), 191-207.

**Positively Curved Manifolds With Large Spherical Rank**

(with B. Schmidt and K. Shankar), Commentarii Mathematici Helvetici 91 (2) (2016), 219-251.

**Affine Maps Between CAT(0) Spaces**

(with H. Bennett and C. Mooney), Geometriae Dedicata 180 (2016), 1-16

**Mixing Properties of Commuting Nilmanifold Automorphisms**

(with A. Gorodnik), Acta Mathematica 215 (1) (2015), 127-159

**Exponential Mixing of Nilmanifold Automorphisms**

(with A. Gorodnik), Journal d'Analyse, 123 (2014), 355-396.

**Global Rigidity of Higher Rank Anosov Actions on Tori and Nilmanifolds**

(with D. Fisher and B. Kalinin), JAMS v. 26 (2013), 167-198.

**Totally non-symplectic Anosov actions on Tori and Nilmanifolds**

(with D. Fisher and B. Kalinin), Geometry & Topology 15 (2011), 191-216.

**Regularity of conjugacies of algebraic actions of Zariski dense groups**

(with A. Gorodnik and T. J. Hitchman), J. Mod. Dyn. 2 (2008), no. 3, 509-540.

**On the Classification of Cartan Actions**

(with B. Kalinin), GAFA v. 17 (2007), p. 468-490.

**Spherical rank rigidity and Blaschke manifolds**

(with K. Shankar and B. Wilking), Duke J. Math. v. 128, 2005

**Measurable rigidity for higher rank abelian actions**

(with B. Kalinin), Ergodic Th. and Dynam. Systems, v. 25, 2005, p. 175-200

**An Invitation to Rigidity Theory**

in: Modern Dynamical Systems and Applications (ed. M. Brin, B. Hasselblatt, Y.
Pesin), p. 211-231, Cambridge University Press 2004

**Smooth classification of Cartan actions of higher rank semisimple Lie
groups and their lattices**

(with E. Goetze), Annals of Mathematics, 150 (1999), 743--773.

**Differential Rigidity of Anosov Actions of Higher Rank Abelian Groups and
Algebraic Lattice Actions**

(with A. Katok), Dynamical systems and related topics, Proceedings of Steklov
Math. Institute, v. 216, 1997, 287--314,
(Editors A.A.Bolibruch, A.M. Stepin, V.V.Ryzhikov).

**On Livsic's theorem, superrigidity, and Anosov actions of semisimple Lie
groups**

(with E. Goetze), Duke Math. J. 88 (1997), 1--27.

**Non-stationary normal forms and rigidity of group actions**

(with A. Katok), Elect. Res. Ann. of the AMS 2 (1996), no. 3, 124-133.

**Invariant measures for higher rank hyperbolic Abelian actions**

(with A. Katok), Ergod. Th. and Dynam. Syst. 16 (1996), 751--778

**Corrections **(PDF
file).

**Harmonic analysis in rigidity theory**

Ergodic Theory and Its Connections With Harmonic Analysis, (Alexandria 1993),
153--205,

London Math. Soc. Lecture Note Ser. 205, Cambridge University Press, Cambridge,
1995.

**First Cohomology of Anosov Actions of Higher Rank Abelian Groups And Applications
to Rigidity**

(with A. Katok), Publ. Math. IHES. 79 (1994), 131--156.

**Errata **(PDF
file)

**New examples of manifolds with completely integrable geodesic flows**

(with G. Paternain), Advances in Math. 108, (1994), 346--366.

**Subelliptic estimates of polynomial differential operators and
applications to rigidity of Abelian actions**

(with A. Katok), Math. Res. Letters 1 (1994), 1--11.

**Riemannian manifolds with completely integrable geodesic flows**

Proc. Symp. Pure Math. 54 (1993), Part 3, (ed. R. E. Greene, S.-T. Yau),
599--608.

**Fundamental groups of negatively curved manifolds and actions of semisimple
groups**

(with R. J. Zimmer), Topology 30 (1991), 591--601.

**Some examples of higher rank manifolds of nonnegative curvature**

(with M. Strake), Comment. Math. Helv. 65 (1990), 299--317.

**Geometrically Finite Groups, Patterson-Sullivan measures and Ratner's
theorem**

(with L. Flaminio), Invent. Math. 99 (1990), 601--626.

**Kazhdan groups, cocycles and trees**

(with S. Adams), Amer. J. of Math. 112 (1990), 271--287.

**On isospectral locally symmetric spaces and a theorem of von Neumann**

Duke Math. J. 59 (1989), 289--294.
** Correction** Duke Math. J. 60 (1990), 561

**Ratner's rigidity theorem for geometrically finite groups**

(with L. Flaminio), in: J. C. Alexander (ed.), Dynamical Systems, Proceedings,
(University of Maryland, 1986/87),

Lecture Notes in Mathematics 1342, 180--195.

**Infinite Coxeter groups do not have Kazhdan's property**

(with M. Bozejko and T. Januszkiewicz), J. of Operator Theory 19 (1988),
63--67.

**An example of an amenable action from geometry**

Ergod. Th. & Dynam. Syst. 7 (1987), 289--293.

**Manifolds of nonpositive curvature and their buildings**

(with K. Burns), Publ. Math. IHES 65 (1987), 35--59.

**On topological Tits buildings and their classification**

(with K. Burns), Publ. Math. IHES 65 (1987), 5--34.

**Structure of manifolds of nonpositive curvature II**

(with W. Ballmann and M. Brin), Annals of Math. 122 (1985), 204--234.

**Lattices acting on boundaries of semisimple groups**

Ergod. Th. and Dynam. Syst. 1 (1981), 489--494.

**Dynamical Properties of Algebraic Systems**

Ph.D. Thesis, University of Warwick 1983.