**Rigidity of compact rank one symmetric spaces**,

with Chris Connell, Mitul Islam and Thang Nguyen, 2024

**Local C^0-rigidity of lattice actions on boundaries,**with Chris Connell, Mitul Islam and Thang Nguyen, 2023

**Anosov actions: classification and the Zimmer Program**,

with Danijela Damjanovic, Kurt Vinhage and Disheng Xu, 2022

**Cartan actions of higher rank abelian groups and their classification**,

with K. Vinhage **Journal of the American Mathematical Society**, 37 (3), 2024, 731–859

https://doi.org/10.1090/jams/1033.

**Anatole Katok’s work on cohomology and geometric rigidity**, ** The Collected Works of Anatole Katok** vol. II, 2024.

**Carnot metrics, dynamics and local r**i**gidity**,

with Chris Connell and Thang Nguyen*Ergodic Theory Dynam. Systems*, *42(2):614–664, 2022.*

**Almost Isotropic Kaehler Manifolds**

with B. Schmidt and K. Shankar**J. Reine Angew. Math., ****767 **(2020), 1–16.

** Hyperbolic rank rigidity for manifolds of 1/4-pinched negative curvature**with C. Connell and T. Nguyen

*Ergodic Theory and Dynamical Systems,*

**40****(5)**

**, 1194-1216, 2018.**** Smooth Factors of Projective Actions of Higher Rank Lattices and Rigidity**with A. Gorodnik

*Geometry and Topology 22 (2018), 1227-1266.***Character Varieties and Actions on Products of Trees**with D. Fisher, M. Larsen and M. Stover

**Israel Journal of Mathematics**225 (2018), 889–907.**Exponential Mixing and Smooth Classification of Commuting Expanding Maps**with L. Yang

**Journal of Modern Dynamics**11 (2017), 263-312.**Equilibrium Measures for Certain Isometric Extensions of Anosov Systems**with D. Visscher

**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

**Journal of the American Mathematical Society**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

**(PDF file**

Corrections*Ergod. Th. and Dynam. Syst. 16 (1996), 751–778*Corrections

**).****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.*(PDF file)

Errata

**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.**with S. Adams**

**Kazhdan groups, cocycles and trees**

**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.*