Papers by Alex Furman

Papers and Preprints by Alex Furman

• Lyapunov spectrum via boundary theory I (with U. Bader)
  preprint [ pdf | arXiv:2504.09731 ]
  
  

• Arithmeticity of hyperbolic groups and marked length pattern rigidity (with Y. Hao)
  preprint [ pdf | arXiv:2209.???? ]
  
  

• Quotients of Poisson boundaries, Entropy, and Spectral Gap (with S. Dodds)
  preprint [ pdf | arXiv:2504.09926 ]
  
  

• Hyperbolic actions of higher-rank lattices come from rank-one factors (with U. Bader, P.E. Caprace, A. Sisto)
  Ergod. Th. Dynam. Syst., 44 (2024), no. 1, 1 – 28 [ pdf | arXiv:2206.06431 ]
  
  

• Quasi-Fuchsian vs Negative Curvature metrics on surface groups (with E. Fricker)
  Israel J. Math., 251 (2022) 365 - 378 [ published-pdf | arXiv:2108.07947 ]
  
  

• An extension of Margulis' Super-Rigidity Theorem (with U. Bader)
  in "Dynamics, Geometry and Number Theory: the Impact of Margulis on Modern Mathematics", University of Chicago Press, Chicago, IL, 2022, 47 -- 65 [ pdf | arXiv:1810.01607 ]
  
  

• Margulis' Super-Rigidity for non-lattice (with U. Bader)
  preprint. [ pdf | arXiv:1810.01608 ]
  
  

• Super-Rigidity and non-linearity for lattices in products (with U. Bader)
  Compos. Math., 156 (2020), no. 1, 158 - 178 [ pdf | arXiv:1802.09931 ]
  
  

• Lattice envelopes (with U. Bader and R. Sauer)
  Duke Math. J., 169 (2020), no. 2, 213 - 278 [ published-pdf | pdf | arXiv:1711.08410 ]
  
  

• Some ergodic properties of metrics on hyperbolic groups (with U. Bader)
  preprint. [ pdf | arXiv:1707.02020 ]
  
  

• An adelic arithmeticity theorem for lattices in products (with U. Bader and R. Sauer)
  Math. Z., 293 (3-4) (2019), 1181 - 1199. [ published-pdf | pdf | arXiv:1705.08158 ]
  
  

• Asymptotic shapes for ergodic families of metrics on nilpotent groups (with M. Cantrell)
  Groups, Geom., Dynam., 11 (2017), no. 4, 1307 - 1345. [ published-pdf | pdf | arXiv:1508.00244 ]
  
  

• On the structure and arithmeticity of lattice envelopes (with U. Bader and R. Sauer)
  C. R. Acad. Sci. Paris, Ser. I, 353 (2015), pp. 409 - 413 [ published-pdf | pdf | arXiv:1411.7332 ]
  
  

• Boundaries, rigidity of representations, and Lyapunov exponents (with U. Bader)
  Proceedings of ICM 2014, Invited Lectures, (2014), 71 - 96. [ pdf | arxiv:1404.5107 ]
  
  

• Algebraic representations of ergodic actions and super-rigidity (with U. Bader)
  preprint (not for publication) [ pdf | arXiv:1311.3696 ]
  
  

• A brief introduction to Ergodic Theory
  Lecture notes (not for publication), pp. 29 [ pdf ]
  
  

• Weak notions of normality and vanishing up to rank in L2-cohomology (with U. Bader and R. Sauer)
  Int. Math. Res. Not. IMRN (2014), no. 12, 3177 - 3189. doi: 10.1093/imrn/rnt029 [ published-pdf | pdf | arXiv:1206.4793 ]
  
  

• Rigidity of group actions on homogeneous spaces, III (with U. Bader, A. Gorodnik, B. Weiss)
  Duke Math. J., 164, vol 1, (2015), 115 - 155. [ pdf | arxiv:1201.5367 ]
  
  

• Boundaries, Weyl groups, and Superrigidity (with U. Bader)
  Electron. Res. Announc. Math. Sci., vol 19 (2012), 41 - 48. [ pdf | arxiv:1109.3482 ]
  
  

• What is a ... stationary measure
  Notices of the AMS 58 iss. 09 (2011), 1276 - 1277. [ pdf | published-pdf ]
  
  

• Integrable measure equivalence and rigidity of hyperbolic lattices (with U. Bader and R. Sauer)
  Invent. Math. 194 (2013), no. 2, 313 - 379. [ pdf | published-pdf | arxiv:1006.5193 ]
  
  

• Stationary measures and equidistribution for orbits of nonabelian semigroups on the torus (with J. Bourgain, E. Lindenstrauss, S. Mozes)
  J. Amer. Math. Soc. 24 (2011), pp. 231 -- 280. [ pdf ]
  
  

• Efficient subdivision in hyperbolic groups and applications (with U. Bader and R. Sauer)
  Groups Geom. Dyn. 7 (2013), no. 2, 263 - 292. [ pdf | arXiv:1003.1562 ]
  
  

• A survey of Measured Group Theory in  "Geometry, Rigidity, and Group Actions"
  The University of Chicago Press, Chicago and London, 2011, 296 - 374 [ published-pdf | pdf | arxiv:0901.0678 ]
  
  

• Superrigidity via Weyl groups: hyperbolic-like targets (with U. Bader)
  coming soon. [ abstract ]
  
  

• Product groups acting on Manifolds (with N. Monod)
  Duke Math. Journal 148 no.1 (2009), 1 - 39. [ pdf | arXiv:0710.3119v2 ]
  
  

• Rigidity of group actions on infinite volume homogeneous spaces, II
  J. Amer. Math. Soc. 21 (2008), 479 - 512. [ pdf | math.DS/0605273 ]
  
  

• Invariant measures and stiffness for non Abelian groups of toral automorphisms (with J. Bourgain, E. Lindenstrauss, S. Mozes)
  C. R. Acad. Sci. Paris, Ser. I, 344 (2007) 737 - 742. [ pdf ]
  
  

• On Popa's Cocycle Superrigidity Theorem
  Inter. Math. Res. Notices IMRN, 2007 (2007), 1 - 46, Art. ID rnm073. [ pdf | math.DS/0608364 ]
  
  

• Superrigidity via Weyl groups: actions on the circle (with U. Bader and Ali Shaker)
  preprint, 38 pages. [ pdf | math.DS/0605276 ]
  
  

• Property (T) and rigidity for actions on Banach spaces (with U. Bader, T. Gelander, and N. Monod)
  Acta Math. 198 (2007), 57 - 105. [ pdf | math.GR/0506361 | abstract ]
  
  

• Outer automorphism groups of some ergodic equivalence relations
  Comment. Math. Helv. 80 (2005), no. 1, 157 - 196. [ pdf | published-pdf | math.DS/0312346 | abstract ]
  
  

• On minimal strongly proximal actions of locally compact groups
  Israel J. Math. 136 (2003), 173 - 187. [ dvi | pdf ]
  
  

• Random walks on groups and random transformations
  Handbook of dynamical systems, Vol. 1A, 931 - 1014, North-Holland, Amsterdam, 2002. [ dvi | pdf ]
  
  

• Coarse-geometric perspective on negatively curved manifolds and groups
  in Rigidity in dynamics and geometry (Cambridge, 2000), 149 - 166, Springer, Berlin, 2002. [ dvi | pdf ]
  
  

• Mostow-Margulis rigidity with locally compact targets
  GAFA, Geom. Func. Anal. 11 (2001), 30 - 59. [ dvi | pdf ]
  
  

• Smooth dynamical systems with discrete spectrum
  Appendix to the paper by R. Gunesch and A. Katok: Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure
  Discr. Cont. Dynam. Syst. 6 No 1, (2000), 61 - 88. [ dvi ]
  
  

• Gromov's measure equivalence and rigidity of higher rank lattices
  Ann. of Math. (2) 150 (1999), 1059 - 1081. [ dvi | pdf | math.GR/9911262 ]
  
  

• Orbit equivalence rigidity
  Ann. of Math. (2) 150 (1999), 1083 - 1108. [ dvi | pdf | math.GR/9911263 ]
  
  

• Sharp ergodic theorems for group actions and strong ergodicity (with Y. Shalom)
  Ergodic Theory Dynam. Systems 19 (1999), no. 4, 1037 - 1061. [ dvi | pdf ]
  
  

• On the ergodic properties of Cartan flows in ergodic actions of SL(2,R) and SO(n,1) (with B. Weiss)
  Ergodic Theory Dynam. Systems 17 (1997), no. 6, 1371 - 1382. [ pdf ]
  
  

• On the multiplicative ergodic theorem for uniquely ergodic systems
  Ann. Inst. H. Poincare Probab. Statist. 33 (1997), no. 6, 797 - 815. [ pdf ]