**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, JAMS, 1-129, 2023.

**Anatole Katok’s work on cohomology and geometric rigidity**,

to appear in:** The Collected Works of Anatole Katok** vol. II, 2021.

**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

*JMD 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

*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

**(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.*